- number: "1"
  prize: "$500"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A276661"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["number theory", "additive combinatorics"]

- number: "2"
  prize: "$1000"
  informal_status:
    state: "disproved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "disproved"
    last_update: "2025-08-31"
  formalized:
    state: "no"
    last_update: "2025-08-31"
  oeis: ["A160559"]
  tags: ["number theory", "covering systems"]

- number: "3"
  prize: "$5000"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A003002", "A003003", "A003004", "A003005"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["number theory", "additive combinatorics", "arithmetic progressions"]

- number: "4"
  prize: "$10000"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  tags: ["number theory", "primes"]
  oeis: ["A002386"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"

- number: "5"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A001223"]
  formalized:
    state: "yes"
    last_update: "2026-08-09"
  tags: ["number theory", "primes"]

- number: "6"
  prize: "$100"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["A335277"]
  formalized:
    state: "yes"
    last_update: "2025-09-18"
  tags: ["number theory", "primes"]

- number: "7"
  prize: "no"
  informal_status:
    state: "verifiable"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "verifiable"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-04-20"
  tags: ["number theory", "covering systems"]

- number: "8"
  prize: "no"
  informal_status:
    state: "disproved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "disproved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory", "covering systems"]

- number: "9"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A006286"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["number theory", "additive basis", "primes"]

- number: "10"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A387053"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["number theory", "additive basis", "primes"]

- number: "11"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2026-03-14"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2026-03-14"
  oeis: ["A001220", "A377587"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["number theory", "additive basis"]

- number: "12"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "13"
  prize: "$100"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["A002264"]
  formalized:
    state: "yes"
    last_update: "2026-02-02"
  tags: ["number theory"]

- number: "14"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A143824", "possible"]
  formalized:
    state: "yes"
    last_update: "2025-11-02"
  tags: ["number theory", "sidon sets", "additive combinatorics"]

- number: "15"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-04-17"
  tags: ["number theory", "primes"]

- number: "16"
  prize: "no"
  informal_status:
    state: "disproved"
    last_update: "2026-02-24"
  formal_status:
    state: "Lean"
    last_update: "2026-02-24"
  status:
    state: "disproved (Lean)"
    last_update: "2026-02-24"
  oeis: ["A006285"]
  formalized:
    state: "yes"
    last_update: "2026-05-26"
  tags: ["number theory", "additive basis", "primes"]

- number: "17"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A038133"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  comments: "cluster primes"
  tags: ["number theory", "primes"]

- number: "18"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A005153"]
  formalized:
    state: "yes"
    last_update: "2026-03-15"
  comments: "practical numbers"
  tags: ["number theory", "divisors", "factorials"]

- number: "19"
  prize: "$500"
  informal_status:
    state: "decidable"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "decidable"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory", "chromatic number"]

- number: "20"
  prize: "$1000"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A332077"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  comments: "sunflower conjecture"
  tags: ["combinatorics"]

- number: "21"
  prize: "$500"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["A391599"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["combinatorics", "intersecting family"]

- number: "22"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "yes"
    last_update: "2026-06-20"
  tags: ["graph theory"]

- number: "23"
  prize: "no"
  informal_status:
    state: "falsifiable"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "falsifiable"
    last_update: "2025-08-31"
  oeis: ["A389646"]
  formalized:
    state: "yes"
    last_update: "2026-02-17"
  tags: ["graph theory"]

- number: "24"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2026-04-23"
  formal_status:
    state: "Lean"
    last_update: "2026-04-23"
  status:
    state: "proved (Lean)"
    last_update: "2026-04-23"
  oeis: ["possible"]
  formalized:
    state: "yes"
    last_update: "2026-08-03"
  tags: ["graph theory"]

- number: "25"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-12-28"
  tags: ["number theory"]

- number: "26"
  prize: "no"
  informal_status:
    state: "disproved"
    last_update: "2025-12-28"
  formal_status:
    state: "Lean"
    last_update: "2025-12-28"
  status:
    state: "disproved (Lean)"
    last_update: "2025-12-28"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-11-25"
  tags: ["number theory", "divisors"]

- number: "27"
  prize: "$100"
  informal_status:
    state: "disproved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "disproved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory", "covering systems"]

- number: "28"
  prize: "$500"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["number theory", "additive basis"]

- number: "29"
  prize: "$100"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory", "additive basis"]

- number: "30"
  prize: "$1000"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A143824", "A227590", "A003022"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["number theory", "sidon sets", "additive combinatorics"]

- number: "31"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-11-24"
  formal_status:
    state: "Lean"
    last_update: "2025-11-24"
  status:
    state: "proved (Lean)"
    last_update: "2025-11-24"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-07-06"
  tags: ["number theory", "additive basis"]

- number: "32"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-02-13"
  tags: ["number theory", "additive basis"]

- number: "33"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-09-04"
  tags: ["number theory", "additive basis"]

- number: "34"
  prize: "no"
  informal_status:
    state: "disproved"
    last_update: "2026-02-05"
  formal_status:
    state: "Lean"
    last_update: "2026-02-05"
  status:
    state: "disproved (Lean)"
    last_update: "2026-02-05"
  oeis: ["A389241", "A234813", "A390187"]
  formalized:
    state: "yes"
    last_update: "2026-07-06"
  tags: ["number theory"]

- number: "35"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory", "additive basis"]

- number: "36"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A393584", "possible"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  comments: "minimum overlap problem"
  tags: ["number theory", "additive combinatorics"]

- number: "37"
  prize: "no"
  informal_status:
    state: "disproved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "disproved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory", "additive combinatorics"]

- number: "38"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2026-05-01"
  formal_status:
    state: "Lean"
    last_update: "2026-05-01"
  status:
    state: "proved (Lean)"
    last_update: "2026-05-01"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-12-20"
  tags: ["number theory"]

- number: "39"
  prize: "$500"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["number theory", "sidon sets", "additive combinatorics"]

- number: "40"
  prize: "$500"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["number theory", "additive basis"]

- number: "41"
  prize: "$500"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["number theory", "sidon sets", "additive combinatorics"]

- number: "42"
  prize: "no"
  informal_status:
    state: "solved"
    last_update: "2026-05-10"
  formal_status:
    state: "Lean"
    last_update: "2026-05-10"
  status:
    state: "solved (Lean)"
    last_update: "2026-05-10"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-10-20"
  tags: ["number theory", "sidon sets", "additive combinatorics"]

- number: "43"
  prize: "$100"
  informal_status:
    state: "disproved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "disproved"
    last_update: "2025-08-31"
  oeis: ["A143824", "A227590", "A003022", "possible"]
  formalized:
    state: "yes"
    last_update: "2026-05-21"
  tags: ["number theory", "sidon sets", "additive combinatorics"]

- number: "44"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["number theory", "sidon sets", "additive combinatorics"]

- number: "45"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2026-05-06"
  formal_status:
    state: "Lean"
    last_update: "2026-05-06"
  status:
    state: "proved (Lean)"
    last_update: "2026-05-06"
  oeis: ["possible"]
  formalized:
    state: "yes"
    last_update: "2026-08-03"
  tags: ["number theory", "unit fractions", "ramsey theory"]

- number: "46"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-12-29"
  formal_status:
    state: "Lean"
    last_update: "2025-12-29"
  status:
    state: "proved (Lean)"
    last_update: "2025-12-29"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-08-03"
  tags: ["number theory", "unit fractions", "ramsey theory"]

- number: "47"
  prize: "$100"
  informal_status:
    state: "proved"
    last_update: "2025-11-28"
  formal_status:
    state: "Lean"
    last_update: "2025-11-28"
  status:
    state: "proved (Lean)"
    last_update: "2025-11-28"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-07-06"
  tags: ["number theory", "unit fractions"]

- number: "48"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "49"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["A365339", "A365474"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory", "primes"]

- number: "50"
  prize: "$250"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-03-19"
  tags: ["number theory"]

- number: "51"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A002202", "A014197"]
  formalized:
    state: "yes"
    last_update: "2025-09-25"
  tags: ["number theory"]

- number: "52"
  prize: "$250"
  informal_status:
    state: "open"
    last_update: "2026-05-28"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2026-05-28"
  oeis: ["A263996"]
  formalized:
    state: "yes"
    last_update: "2026-04-17"
  comments: "sum-product problem"
  tags: ["number theory", "additive combinatorics"]

- number: "53"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory", "additive combinatorics"]

- number: "54"
  prize: "$100"
  informal_status:
    state: "solved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "solved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory", "ramsey theory"]

- number: "55"
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    state: "solved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "solved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory", "ramsey theory"]

- number: "56"
  prize: "$10"
  informal_status:
    state: "disproved"
    last_update: "2025-11-26"
  formal_status:
    state: "Lean"
    last_update: "2025-11-26"
  status:
    state: "disproved (Lean)"
    last_update: "2025-11-26"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["number theory", "intersecting family"]

- number: "57"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory", "chromatic number", "cycles"]

- number: "58"
  prize: "no"
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    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory", "chromatic number", "cycles"]

- number: "59"
  prize: "no"
  informal_status:
    state: "disproved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "disproved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory", "turan number"]

- number: "60"
  prize: "no"
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    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A006855"]
  formalized:
    state: "yes"
    last_update: "2026-08-03"
  tags: ["graph theory", "cycles"]

- number: "61"
  prize: "no"
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    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-09-30"
  tags: ["graph theory"]

- number: "62"
  prize: "no"
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    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory"]

- number: "63"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory", "chromatic number", "cycles"]

- number: "64"
  prize: "$1000"
  informal_status:
    state: "falsifiable"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "falsifiable"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["graph theory", "cycles"]

- number: "65"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory", "cycles"]

- number: "66"
  prize: "$500"
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    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["number theory", "additive basis"]

- number: "67"
  prize: "$500"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["A181740", "A237695"]
  formalized:
    state: "yes"
    last_update: "2025-11-04"
  comments: "Erdős discrepancy problem"
  tags: ["discrepancy"]


- number: "68"
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    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
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  oeis: ["A331373"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["number theory", "irrationality"]

- number: "69"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-12-02"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-12-02"
  oeis: ["A262153"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["number theory", "irrationality"]

- number: "70"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-06-08"
  tags: ["graph theory", "ramsey theory", "set theory"]

- number: "71"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2026-06-07"
  formal_status:
    state: "Lean"
    last_update: "2026-06-07"
  status:
    state: "proved (Lean)"
    last_update: "2026-06-07"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-07-22"
  tags: ["graph theory", "cycles"]

- number: "72"
  prize: "$100"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory", "cycles"]

- number: "73"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory"]

- number: "74"
  prize: "$500"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-09-25"
  tags: ["graph theory", "chromatic number", "cycles"]

- number: "75"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-04-04"
  tags: ["graph theory", "chromatic number"]

- number: "76"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["A060407"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory", "ramsey theory"]

- number: "77"
  prize: "$250"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A059442"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory", "ramsey theory"]

- number: "78"
  prize: "$100"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A059442"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory", "ramsey theory"]

- number: "79"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory", "ramsey theory"]

- number: "80"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-08-10"
  tags: ["graph theory", "ramsey theory"]

- number: "81"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory"]

- number: "82"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A120414", "A390256", "A390257", "A390919", "A392636", "A394400", "A394462",
    "A394539", "A394563", "A394564", "A394573", "A394574", "A394930", "A394933"]
  formalized:
    state: "yes"
    last_update: "2026-01-17"
  tags: ["graph theory"]

- number: "83"
  prize: "$500"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["A071799", "A387635"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["combinatorics"]

- number: "84"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory", "cycles"]

- number: "85"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2026-03-14"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2026-03-14"
  oeis: ["A006672", "possible"]
  formalized:
    state: "yes"
    last_update: "2025-11-21"
  tags: ["graph theory"]

- number: "86"
  prize: "$100"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A245762"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory"]

- number: "87"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A059442", "possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory", "ramsey theory"]

- number: "88"
  prize: "$100"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory", "ramsey theory"]

- number: "89"
  prize: "$500"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A186704", "A131628"]
  formalized:
    state: "yes"
    last_update: "2025-10-24"
  comments: "Erdős distance problem"
  tags: ["geometry", "distances"]

- number: "90"
  prize: "$500"
  informal_status:
    state: "disproved"
    last_update: "2026-06-07"
  formal_status:
    state: "Lean"
    last_update: "2026-06-07"
  status:
    state: "disproved (Lean)"
    last_update: "2026-06-07"
  oeis: ["A186705"]
  formalized:
    state: "yes"
    last_update: "2025-09-25"
  comments: "unit distance problem"
  tags: ["geometry", "distances"]

- number: "91"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A186704", "possible"]
  formalized:
    state: "yes"
    last_update: "2026-04-16"
  tags: ["geometry", "distances"]

- number: "92"
  prize: "$500"
  informal_status:
    state: "disproved"
    last_update: "2026-05-21"
  formal_status:
    state: "unformalized"
  status:
    state: "disproved"
    last_update: "2026-05-21"
  oeis: ["possible"]
  formalized:
    state: "yes"
    last_update: "2025-09-25"
  tags: ["geometry", "distances"]

- number: "93"
  prize: "no"
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    state: "proved"
    last_update: "2025-02-17"
  formal_status:
    state: "Lean"
    last_update: "2025-02-17"
  status:
    state: "proved (Lean)"
    last_update: "2025-02-17"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-08-03"
  tags: ["geometry", "convex", "distances"]

- number: "94"
  prize: "£25"
  informal_status:
    state: "proved"
    last_update: "2026-01-15"
  formal_status:
    state: "Lean"
    last_update: "2026-01-15"
  status:
    state: "proved (Lean)"
    last_update: "2026-01-15"
  oeis: ["A387858"]
  formalized:
    state: "yes"
    last_update: "2026-08-03"
  tags: ["geometry", "convex", "distances"]

- number: "95"
  prize: "$500"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["geometry", "convex", "distances"]

- number: "96"
  prize: "no"
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    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "yes"
    last_update: "2026-05-21"
  tags: ["geometry", "distances", "convex"]

- number: "97"
  prize: "$100"
  informal_status:
    state: "falsifiable"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "falsifiable"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-11-11"
  tags: ["geometry", "distances", "convex"]

- number: "98"
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  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "yes"
    last_update: "2026-05-23"
  tags: ["geometry", "distances"]

- number: "99"
  prize: "$100"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-01-15"
  tags: ["geometry", "distances"]

- number: "100"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-01-25"
  tags: ["geometry", "distances"]

- number: "101"
  prize: "$100"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A006065", "possible"]
  formalized:
    state: "yes"
    last_update: "2026-04-16"
  tags: ["geometry"]

- number: "102"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["geometry"]

- number: "103"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["geometry", "distances"]

- number: "104"
  prize: "$100"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A003829"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["geometry"]

- number: "105"
  prize: "$50"
  informal_status:
    state: "disproved"
    last_update: "2025-11-22"
  formal_status:
    state: "Lean"
    last_update: "2025-11-22"
  status:
    state: "disproved (Lean)"
    last_update: "2025-11-22"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-08-03"
  tags: ["geometry"]

- number: "106"
  prize: "no"
  informal_status:
    state: "falsifiable"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "falsifiable"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["geometry"]

- number: "107"
  prize: "$500"
  informal_status:
    state: "falsifiable"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "falsifiable"
    last_update: "2025-08-31"
  oeis: ["A000051"]
  formalized:
    state: "yes"
    last_update: "2025-09-29"
  comments: "'Happy Ending' problem"
  tags: ["geometry", "convex"]

- number: "108"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "yes"
    last_update: "2025-11-24"
  tags: ["graph theory", "chromatic number", "cycles"]

- number: "109"
  prize: "no"
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    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
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  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-01-12"
  comments: "Erdős sumset conjecture"
  tags: ["additive combinatorics"]

- number: "110"
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    state: "disproved"
    last_update: "2026-04-05"
  formal_status:
    state: "unformalized"
  status:
    state: "disproved"
    last_update: "2026-04-05"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory", "chromatic number", "cycles"]

- number: "111"
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    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory", "chromatic number", "set theory"]

- number: "112"
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    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory", "ramsey theory"]

- number: "113"
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  informal_status:
    state: "disproved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "disproved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory", "turan number"]

- number: "114"
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    state: "falsifiable"
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  formal_status:
    state: "unformalized"
  status:
    state: "falsifiable"
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  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["polynomials", "analysis"]

- number: "115"
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    state: "proved"
    last_update: "2026-03-03"
  formal_status:
    state: "Lean"
    last_update: "2026-03-03"
  status:
    state: "proved (Lean)"
    last_update: "2026-03-03"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-08-03"
  tags: ["polynomials", "analysis"]

- number: "116"
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    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["polynomials", "analysis"]

- number: "117"
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    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["group theory"]

- number: "118"
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  informal_status:
    state: "disproved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "disproved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["set theory", "ramsey theory"]

- number: "119"
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  informal_status:
    state: "solved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "solved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-11-27"
  tags: ["analysis", "polynomials"]

- number: "120"
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  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-01-23"
  comments: "Erdős similarity problem"
  tags: ["combinatorics"]

- number: "121"
  prize: "no"
  informal_status:
    state: "disproved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "disproved"
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  oeis: ["A028391", "A013928", "A372306", "A373319", "A372306", "A373178", "A360659",
    "A373114", "A143301"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory", "squares"]

- number: "122"
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    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "123"
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    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "Lean"
    last_update: "2025-08-31"
  status:
    state: "proved (Lean)"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-12-17"
  tags: ["number theory"]

- number: "124"
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    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-11-12"
  tags: ["number theory", "base representations"]

- number: "125"
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    state: "disproved"
    last_update: "2026-03-30"
  formal_status:
    state: "Lean"
    last_update: "2026-03-30"
  status:
    state: "disproved (Lean)"
    last_update: "2026-03-30"
  oeis: ["A367090"]
  formalized:
    state: "yes"
    last_update: "2025-12-09"
  tags: ["number theory", "base representations"]

- number: "126"
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  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "127"
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  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory"]

- number: "128"
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  informal_status:
    state: "falsifiable"
    last_update: "2025-10-31"
  formal_status:
    state: "unformalized"
  status:
    state: "falsifiable"
    last_update: "2025-10-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["graph theory"]

- number: "129"
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  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  comments: "ambiguous statement"
  tags: ["graph theory", "ramsey theory"]

- number: "130"
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  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-08-07"
  tags: ["graph theory", "chromatic number"]

- number: "131"
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  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A068063"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "132"
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  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["distances"]

- number: "133"
  prize: "no"
  informal_status:
    state: "disproved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "disproved"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory"]

- number: "134"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2026-02-07"
  formal_status:
    state: "Lean"
    last_update: "2026-02-07"
  status:
    state: "proved (Lean)"
    last_update: "2026-02-07"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-06-26"
  tags: ["graph theory"]

- number: "135"
  prize: "$250"
  informal_status:
    state: "disproved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "disproved"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["distances", "geometry"]

- number: "136"
  prize: "no"
  informal_status:
    state: "solved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "solved"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory"]

- number: "137"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "138"
  prize: "$500"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A005346"]
  formalized:
    state: "yes"
    last_update: "2025-09-29"
  tags: ["additive combinatorics"]

- number: "139"
  prize: "$1000"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["A003002", "A003003", "A003004", "A003005"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  comments: "Szemerédi's theorem"
  tags: ["additive combinatorics", "arithmetic progressions"]

- number: "140"
  prize: "$500"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["A003002"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["additive combinatorics", "arithmetic progressions"]

- number: "141"
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    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A006560"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["additive combinatorics", "primes", "arithmetic progressions"]

- number: "142"
  prize: "$10000"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A003002", "A003003", "A003004", "A003005"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["additive combinatorics", "arithmetic progressions"]

- number: "143"
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    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["primitive sets"]

- number: "144"
  prize: "$250"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["A005279"]
  formalized:
    state: "no"
    last_update: "2025-09-01"
  tags: ["number theory", "divisors"]

- number: "145"
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  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A005117"]
  formalized:
    state: "yes"
    last_update: "2025-10-02"
  tags: ["number theory"]

- number: "146"
  prize: "$500"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "Lean"
    last_update: "2026-08-02"
    url: "https://github.com/openai/ten-proofs/blob/94bc0feb6a9ff12c7d31d6de640a725c9d43d2b6/CompactnessAndDegeneracy.lean#L18543-L18585"
    note: "counterexample; refutes the degeneracy conjecture"
  status:
    state: "open (Lean)"
    last_update: "2026-08-02"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-08-07"
  tags: ["graph theory", "turan number"]

- number: "147"
  prize: "$500"
  informal_status:
    state: "disproved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "disproved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory", "turan number"]

- number: "148"
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  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A076393", "A006585"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory", "unit fractions"]

- number: "149"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory"]

- number: "150"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2026-03-31"
  formal_status:
    state: "Lean"
    last_update: "2026-03-31"
  status:
    state: "proved (Lean)"
    last_update: "2026-03-31"
  oeis: ["possible"]
  formalized:
    state: "yes"
    last_update: "2026-08-03"
  tags: ["graph theory"]

- number: "151"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory"]

- number: "152"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2026-04-03"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2026-04-03"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-01-06"
  tags: ["sidon sets"]

- number: "153"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-01-08"
  tags: ["sidon sets"]

- number: "154"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2026-02-06"
  formal_status:
    state: "Lean"
    last_update: "2026-02-06"
  status:
    state: "proved (Lean)"
    last_update: "2026-02-06"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-06-29"
  tags: ["sidon sets"]

- number: "155"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
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  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["additive combinatorics", "sidon sets"]

- number: "156"
  prize: "no"
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    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A382397"]
  formalized:
    state: "yes"
    last_update: "2026-06-21"
  tags: ["sidon sets"]

- number: "157"
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    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["sidon sets"]

- number: "158"
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    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-01-04"
  tags: ["sidon sets"]

- number: "159"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory", "ramsey theory"]

- number: "160"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["additive combinatorics", "arithmetic progressions"]

- number: "161"
  prize: "$500"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["combinatorics", "ramsey theory", "discrepancy"]

- number: "162"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
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    state: "no"
    last_update: "2025-08-31"
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- number: "163"
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    state: "proved"
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    state: "unformalized"
  status:
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    state: "no"
    last_update: "2025-08-31"
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  tags: ["graph theory", "ramsey theory"]

- number: "164"
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    state: "proved"
    last_update: "2026-04-23"
  formal_status:
    state: "Lean"
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  status:
    state: "proved (Lean)"
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    state: "yes"
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  tags: ["number theory", "primitive sets"]

- number: "165"
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    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A000791"]
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    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory", "ramsey theory"]

- number: "166"
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    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
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  oeis: ["A059442"]
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    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory", "ramsey theory"]

- number: "167"
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    state: "falsifiable"
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  formal_status:
    state: "unformalized"
  status:
    state: "falsifiable"
    last_update: "2025-09-28"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory"]

- number: "168"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A004059", "A057561", "A094708", "A386439"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["additive combinatorics"]

- number: "169"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A005346"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["additive combinatorics", "arithmetic progressions"]

- number: "170"
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  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A046693"]
  formalized:
    state: "yes"
    last_update: "2025-11-25"
  comments: "sparse ruler problem"
  tags: ["additive combinatorics"]

- number: "171"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["A156989"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  comments: "density Hales-Jewett"
  tags: ["additive combinatorics", "combinatorics"]

- number: "172"
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  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-11-25"
  tags: ["additive combinatorics", "ramsey theory"]

- number: "173"
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    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["geometry", "ramsey theory"]

- number: "174"
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    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["geometry", "ramsey theory"]

- number: "175"
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    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
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- number: "176"
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    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
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    state: "no"
    last_update: "2025-08-31"
  tags: ["additive combinatorics", "arithmetic progressions", "discrepancy"]

- number: "177"
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    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["discrepancy", "arithmetic progressions"]

- number: "178"
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    state: "proved"
    last_update: "2026-04-21"
  formal_status:
    state: "Lean"
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  status:
    state: "proved (Lean)"
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  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-06-26"
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- number: "179"
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    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
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    state: "no"
    last_update: "2025-08-31"
  tags: ["additive combinatorics", "arithmetic progressions"]

- number: "180"
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  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "Lean"
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    note: "counterexample; refutes the compactness conjecture"
  status:
    state: "open (Lean)"
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  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-08-07"
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- number: "181"
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    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
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    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory", "ramsey theory"]

- number: "182"
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    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["possible"]
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    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory"]

- number: "183"
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    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "Lean"
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    state: "open"
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  formal_status:
    state: "unformalized"
  status:
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- number: "185"
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    state: "proved"
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  formal_status:
    state: "unformalized"
  status:
    state: "proved"
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  oeis: ["A003142"]
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    last_update: "2025-08-31"
  tags: ["additive combinatorics"]

- number: "186"
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    state: "solved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "solved"
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    state: "no"
    last_update: "2025-08-31"
  tags: ["additive combinatorics"]

- number: "187"
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    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
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- number: "188"
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    state: "open"
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  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
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  formalized:
    state: "yes"
    last_update: "2025-09-23"
  tags: ["geometry", "ramsey theory"]

- number: "189"
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    state: "disproved"
    last_update: "2025-12-19"
  formal_status:
    state: "Lean"
    last_update: "2025-12-19"
  status:
    state: "disproved (Lean)"
    last_update: "2025-12-19"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["geometry", "ramsey theory"]

- number: "190"
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    state: "solved"
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  formal_status:
    state: "unformalized"
  status:
    state: "solved"
    last_update: "2026-06-02"
  oeis: ["possible"]
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    state: "no"
    last_update: "2025-08-31"
  tags: ["additive combinatorics", "arithmetic progressions"]

- number: "191"
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    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["combinatorics", "ramsey theory"]

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    state: "solved"
    last_update: "2026-05-14"
  formal_status:
    state: "Lean"
    last_update: "2026-05-14"
  status:
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    last_update: "2026-05-14"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["arithmetic progressions", "combinatorics"]

- number: "193"
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    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A231255"]
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    state: "yes"
    last_update: "2026-03-05"
  tags: ["geometry"]

- number: "194"
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    state: "disproved"
    last_update: "2026-04-19"
  formal_status:
    state: "Lean"
    last_update: "2026-04-19"
  status:
    state: "disproved (Lean)"
    last_update: "2026-04-19"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-01-17"
  tags: ["arithmetic progressions"]

- number: "195"
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    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-01-18"
  tags: ["arithmetic progressions"]

- number: "196"
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    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-09-04"
  tags: ["arithmetic progressions"]

- number: "197"
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    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-01-20"
  tags: ["arithmetic progressions"]

- number: "198"
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    state: "disproved"
    last_update: "2025-11-23"
  formal_status:
    state: "Lean"
    last_update: "2025-11-23"
  status:
    state: "disproved (Lean)"
    last_update: "2025-11-23"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["additive combinatorics", "sidon sets", "arithmetic progressions"]

- number: "199"
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    state: "disproved"
    last_update: "2026-02-24"
  formal_status:
    state: "Lean"
    last_update: "2026-02-24"
  status:
    state: "disproved (Lean)"
    last_update: "2026-02-24"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-07-02"
  tags: ["arithmetic progressions"]

- number: "200"
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    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A005115"]
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    state: "yes"
    last_update: "2025-08-31"
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- number: "201"
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    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A003002", "A003003", "A003004", "A003005", "possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["additive combinatorics", "arithmetic progressions"]

- number: "202"
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    state: "solved"
    last_update: "2026-05-14"
  formal_status:
    state: "Lean"
    last_update: "2026-05-14"
  status:
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    last_update: "2026-05-14"
  oeis: ["A389975"]
  formalized:
    state: "yes"
    last_update: "2026-08-03"
  tags: ["covering systems"]

- number: "203"
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    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
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  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["primes", "covering systems"]

- number: "204"
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    state: "disproved"
    last_update: "2026-03-15"
  formal_status:
    state: "Lean"
    last_update: "2026-03-15"
  status:
    state: "disproved (Lean)"
    last_update: "2026-03-15"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-01-17"
  tags: ["covering systems"]

- number: "205"
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    state: "disproved"
    last_update: "2026-01-10"
  formal_status:
    state: "Lean"
    last_update: "2026-01-10"
  status:
    state: "disproved (Lean)"
    last_update: "2026-01-10"
  oeis: ["possible"]
  formalized:
    state: "yes"
    last_update: "2026-08-03"
  tags: ["number theory"]

- number: "206"
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  informal_status:
    state: "disproved"
    last_update: "2026-04-28"
  formal_status:
    state: "Lean"
    last_update: "2026-04-28"
  status:
    state: "disproved (Lean)"
    last_update: "2026-04-28"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-07-22"
  tags: ["number theory", "unit fractions"]

- number: "207"
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    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["combinatorics", "hypergraphs"]

- number: "208"
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    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
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    state: "yes"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "209"
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    state: "disproved"
    last_update: "2026-06-21"
  formal_status:
    state: "Lean"
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  status:
    state: "disproved (Lean)"
    last_update: "2026-06-21"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-07-22"
  tags: ["geometry"]

- number: "210"
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    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["A003034"]
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    state: "no"
    last_update: "2025-08-31"
  tags: ["geometry"]

- number: "211"
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    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["geometry"]

- number: "212"
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  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["geometry", "distances"]

- number: "213"
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    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
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  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["geometry", "distances"]

- number: "214"
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    state: "proved"
    last_update: "2026-02-03"
  formal_status:
    state: "Lean"
    last_update: "2026-02-03"
  status:
    state: "proved (Lean)"
    last_update: "2026-02-03"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-08-03"
  tags: ["geometry", "distances"]

- number: "215"
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  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["geometry"]

- number: "216"
  prize: "no"
  informal_status:
    state: "disproved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "disproved"
    last_update: "2025-08-31"
  oeis: ["A381776"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["geometry", "convex"]

- number: "217"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["geometry", "distances"]

- number: "218"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A333230", "A333231", "A064113"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["number theory", "primes"]

- number: "219"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["A005115", "A113827", "A123556"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  comments: "Green-Tao theorem"
  tags: ["number theory", "additive combinatorics", "primes", "arithmetic progressions"]

- number: "220"
  prize: "$500"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["A322144"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "221"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2026-01-31"
  formal_status:
    state: "Lean"
    last_update: "2026-01-31"
  status:
    state: "proved (Lean)"
    last_update: "2026-01-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-07-02"
  tags: ["number theory", "additive basis"]

- number: "222"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A001481", "A256435"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory", "squares"]

- number: "223"
  prize: "no"
  informal_status:
    state: "solved"
    last_update: "2025-10-14"
  formal_status:
    state: "unformalized"
  status:
    state: "solved"
    last_update: "2025-10-14"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["geometry", "distances"]

- number: "224"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2026-01-14"
  formal_status:
    state: "Lean"
    last_update: "2026-01-14"
  status:
    state: "proved (Lean)"
    last_update: "2026-01-14"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-07-02"
  tags: ["geometry"]

- number: "225"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["analysis"]

- number: "226"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-12-29"
  formal_status:
    state: "Lean"
    last_update: "2025-12-29"
  status:
    state: "proved (Lean)"
    last_update: "2025-12-29"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-07-02"
  tags: ["analysis"]

- number: "227"
  prize: "no"
  informal_status:
    state: "disproved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "disproved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["analysis"]

- number: "228"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["analysis", "polynomials"]

- number: "229"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-12-28"
  formal_status:
    state: "Lean"
    last_update: "2025-12-28"
  status:
    state: "proved (Lean)"
    last_update: "2025-12-28"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["analysis", "iterated functions"]

- number: "230"
  prize: "no"
  informal_status:
    state: "disproved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "disproved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["analysis", "polynomials"]

- number: "231"
  prize: "no"
  informal_status:
    state: "disproved"
    last_update: "2026-05-14"
  formal_status:
    state: "Lean"
    last_update: "2026-05-14"
  status:
    state: "disproved (Lean)"
    last_update: "2026-05-14"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["combinatorics"]

- number: "232"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["geometry", "distances"]

- number: "233"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A074741"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["number theory", "primes"]

- number: "234"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-01-12"
  tags: ["number theory", "primes"]

- number: "235"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "236"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A039669", "A109925"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["number theory", "primes"]

- number: "237"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2026-03-04"
  formal_status:
    state: "Lean"
    last_update: "2026-03-04"
  status:
    state: "proved (Lean)"
    last_update: "2026-03-04"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory", "primes"]

- number: "238"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-01-11"
  tags: ["number theory", "primes"]

- number: "239"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-01-18"
  tags: ["number theory"]

- number: "240"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory", "primes"]

- number: "241"
  prize: "$100"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A387704"]
  formalized:
    state: "yes"
    last_update: "2026-02-25"
  tags: ["additive combinatorics", "sidon sets"]

- number: "242"
  prize: "no"
  informal_status:
    state: "falsifiable"
    last_update: "2025-09-28"
  formal_status:
    state: "unformalized"
  status:
    state: "falsifiable"
    last_update: "2025-09-28"
  oeis: ["A073101", "A075245", "A075246", "A075247", "A075248", "A287116"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  comments: "Erdős-Straus conjecture"
  tags: ["number theory", "unit fractions"]

- number: "243"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A000058"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "244"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["number theory", "primes"]

- number: "245"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["additive combinatorics"]

- number: "246"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-12-28"
  formal_status:
    state: "Lean"
    last_update: "2025-12-28"
  status:
    state: "proved (Lean)"
    last_update: "2025-12-28"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-07-02"
  tags: ["number theory"]

- number: "247"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["number theory", "irrationality"]

- number: "248"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-12-02"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-12-02"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "249"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A256936"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["number theory", "irrationality"]

- number: "250"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["A066766"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["number theory", "irrationality"]

- number: "251"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A098990"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["number theory", "irrationality"]

- number: "252"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A227988", "A227989", "A307036", "A359060", "possible"]
  formalized:
    state: "yes"
    last_update: "2026-01-03"
  tags: ["number theory", "irrationality"]

- number: "253"
  prize: "no"
  informal_status:
    state: "disproved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "disproved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-09-05"
  tags: ["number theory"]

- number: "254"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-03-08"
  tags: ["number theory"]

- number: "255"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["discrepancy"]

- number: "256"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["analysis"]

- number: "257"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["irrationality"]

- number: "258"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2026-04-21"
  formal_status:
    state: "Lean"
    last_update: "2026-04-21"
  status:
    state: "proved (Lean)"
    last_update: "2026-04-21"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["irrationality"]

- number: "259"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2026-04-21"
  formal_status:
    state: "Lean"
    last_update: "2026-04-21"
  status:
    state: "proved (Lean)"
    last_update: "2026-04-21"
  oeis: ["A371134"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["irrationality"]

- number: "260"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-03-09"
  tags: ["irrationality"]

- number: "261"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "262"
  prize: "no"
  informal_status:
    state: "solved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "solved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["irrationality"]

- number: "263"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-01-25"
  tags: ["irrationality"]

- number: "264"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["irrationality"]

- number: "265"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  comments: "ambiguous statement"
  tags: ["irrationality"]

- number: "266"
  prize: "no"
  informal_status:
    state: "disproved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "disproved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-10-03"
  tags: ["irrationality"]

- number: "267"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["irrationality"]

- number: "268"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2026-04-13"
  formal_status:
    state: "Lean"
    last_update: "2026-04-13"
  status:
    state: "proved (Lean)"
    last_update: "2026-04-13"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-12-30"
  tags: ["number theory"]

- number: "269"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-09-02"
  tags: ["irrationality"]

- number: "270"
  prize: "no"
  informal_status:
    state: "disproved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "disproved"
    last_update: "2025-08-31"
  oeis: ["A073016"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["irrationality"]

- number: "271"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A005487"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  comments: "Stanley sequences"
  tags: ["additive combinatorics", "arithmetic progressions"]

- number: "272"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "yes"
    last_update: "2026-04-16"
  tags: ["additive combinatorics", "arithmetic progressions"]

- number: "273"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["number theory", "covering systems"]

- number: "274"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  comments: "Herzog-Schönheim conjecture"
  tags: ["group theory", "covering systems"]

- number: "275"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2026-01-20"
  formal_status:
    state: "Lean"
    last_update: "2026-01-20"
  status:
    state: "proved (Lean)"
    last_update: "2026-01-20"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-01-18"
  tags: ["number theory", "covering systems"]

- number: "276"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-10-21"
  tags: ["number theory", "covering systems"]

- number: "277"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-01-20"
  tags: ["number theory", "covering systems"]

- number: "278"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory", "covering systems"]

- number: "279"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-05-15"
  tags: ["number theory", "covering systems", "primes"]

- number: "280"
  prize: "no"
  informal_status:
    state: "disproved"
    last_update: "2026-04-18"
  formal_status:
    state: "Lean"
    last_update: "2026-04-18"
  status:
    state: "disproved (Lean)"
    last_update: "2026-04-18"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-07-06"
  tags: ["number theory", "covering systems"]

- number: "281"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2026-01-19"
  formal_status:
    state: "Lean"
    last_update: "2026-01-19"
  status:
    state: "proved (Lean)"
    last_update: "2026-01-19"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-07-06"
  tags: ["number theory", "covering systems"]

- number: "282"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-04-16"
  tags: ["number theory", "unit fractions"]

- number: "283"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2026-05-10"
  formal_status:
    state: "Lean"
    last_update: "2026-05-10"
  status:
    state: "proved (Lean)"
    last_update: "2026-05-10"
  oeis: ["A380791"]
  formalized:
    state: "yes"
    last_update: "2025-11-06"
  tags: ["number theory", "unit fractions"]

- number: "284"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory", "unit fractions"]

- number: "285"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["A030659"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["number theory", "unit fractions"]

- number: "286"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory", "unit fractions"]

- number: "287"
  prize: "no"
  informal_status:
    state: "falsifiable"
    last_update: "2025-12-05"
  formal_status:
    state: "unformalized"
  status:
    state: "falsifiable"
    last_update: "2025-12-05"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-06-24"
  tags: ["number theory", "unit fractions"]

- number: "288"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-10-03"
  tags: ["number theory", "unit fractions"]

- number: "289"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["number theory", "unit fractions"]

- number: "290"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2026-01-14"
  formal_status:
    state: "Lean"
    last_update: "2026-01-14"
  status:
    state: "proved (Lean)"
    last_update: "2026-01-14"
  oeis: ["A375081"]
  formalized:
    state: "yes"
    last_update: "2026-06-26"
  tags: ["number theory", "unit fractions"]

- number: "291"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A110566"]
  formalized:
    state: "yes"
    last_update: "2026-06-24"
  tags: ["number theory", "unit fractions"]

- number: "292"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["A092671"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory", "unit fractions"]

- number: "293"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory", "unit fractions"]

- number: "294"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory", "unit fractions"]

- number: "295"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A192881"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["number theory", "unit fractions"]

- number: "296"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2026-04-22"
  formal_status:
    state: "Lean"
    last_update: "2026-04-22"
  status:
    state: "proved (Lean)"
    last_update: "2026-04-22"
  oeis: ["possible"]
  formalized:
    state: "yes"
    last_update: "2026-07-02"
  tags: ["number theory", "unit fractions"]

- number: "297"
  prize: "no"
  informal_status:
    state: "solved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "solved"
    last_update: "2025-08-31"
  oeis: ["A092670"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory", "unit fractions"]

- number: "298"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-12-29"
  formal_status:
    state: "Lean"
    last_update: "2025-12-29"
  status:
    state: "proved (Lean)"
    last_update: "2025-12-29"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["number theory", "unit fractions"]

- number: "299"
  prize: "no"
  informal_status:
    state: "disproved"
    last_update: "2025-12-29"
  formal_status:
    state: "Lean"
    last_update: "2025-12-29"
  status:
    state: "disproved (Lean)"
    last_update: "2025-12-29"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["number theory", "unit fractions"]

- number: "300"
  prize: "no"
  informal_status:
    state: "solved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "solved"
    last_update: "2025-08-31"
  oeis: ["A390393"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory", "unit fractions"]

- number: "301"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A390394"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory", "unit fractions"]

- number: "302"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A390395"]
  formalized:
    state: "yes"
    last_update: "2026-08-05"
  tags: ["number theory", "unit fractions"]

- number: "303"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-12-21"
  formal_status:
    state: "Lean"
    last_update: "2025-12-21"
  status:
    state: "proved (Lean)"
    last_update: "2025-12-21"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["number theory", "unit fractions"]

- number: "304"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A097847", "A097849"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["number theory", "unit fractions"]

- number: "305"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory", "unit fractions"]

- number: "306"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["number theory", "unit fractions"]

- number: "307"
  prize: "no"
  informal_status:
    state: "verifiable"
    last_update: "2025-09-09"
  formal_status:
    state: "unformalized"
  status:
    state: "verifiable"
    last_update: "2025-09-09"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["number theory", "unit fractions"]

- number: "308"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory", "unit fractions"]

- number: "309"
  prize: "no"
  informal_status:
    state: "disproved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "disproved"
    last_update: "2025-08-31"
  oeis: ["A217693"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory", "unit fractions"]

- number: "310"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory", "unit fractions"]

- number: "311"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory", "unit fractions"]

- number: "312"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-09-24"
  tags: ["number theory", "unit fractions"]

- number: "313"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A054377"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["number theory", "unit fractions"]

- number: "314"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "Lean"
    last_update: "2025-08-31"
  status:
    state: "proved (Lean)"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-08-03"
  tags: ["number theory", "unit fractions"]

- number: "315"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2026-01-31"
  formal_status:
    state: "Lean"
    last_update: "2026-01-31"
  status:
    state: "proved (Lean)"
    last_update: "2026-01-31"
  oeis: ["A000058", "A076393"]
  formalized:
    state: "yes"
    last_update: "2026-08-03"
  tags: ["number theory", "unit fractions"]

- number: "316"
  prize: "no"
  informal_status:
    state: "disproved"
    last_update: "2025-09-02"
  formal_status:
    state: "Lean"
    last_update: "2025-09-02"
  status:
    state: "disproved (Lean)"
    last_update: "2025-09-02"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["number theory", "unit fractions"]

- number: "317"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-11-18"
  tags: ["number theory", "unit fractions"]

- number: "318"
  prize: "no"
  informal_status:
    state: "solved"
    last_update: "2026-04-04"
  formal_status:
    state: "unformalized"
  status:
    state: "solved"
    last_update: "2026-04-04"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-01-14"
  tags: ["number theory", "unit fractions"]

- number: "319"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["number theory", "unit fractions"]

- number: "320"
  prize: "no"
  informal_status:
    state: "solved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "solved"
    last_update: "2025-08-31"
  oeis: ["A072207"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory", "unit fractions"]

- number: "321"
  prize: "no"
  informal_status:
    state: "solved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "solved"
    last_update: "2025-08-31"
  oeis: ["A384927", "A391592"]
  formalized:
    state: "yes"
    last_update: "2025-10-06"
  tags: ["number theory", "unit fractions"]

- number: "322"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A025456", "A025418"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory", "powers"]

- number: "323"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A004825", "A004831", "A004832", "A004833", "A004842", "A004843", "A004844",
    "A004845", "A004857", "A004869", "possible"]
  formalized:
    state: "yes"
    last_update: "2026-03-15"
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- number: "324"
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    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
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    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["number theory", "powers"]

- number: "325"
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    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
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    last_update: "2025-08-31"
  oeis: ["A004825", "A004832", "A004843", "A004854", "A004865", "possible"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["number theory", "powers"]

- number: "326"
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    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-09-01"
  tags: ["number theory", "additive basis"]

- number: "327"
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    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A384927"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory", "unit fractions"]

- number: "328"
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    state: "disproved"
    last_update: "2026-06-21"
  formal_status:
    state: "Lean"
    last_update: "2026-06-21"
  status:
    state: "disproved (Lean)"
    last_update: "2026-06-21"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-07-22"
  tags: ["number theory", "additive combinatorics"]

- number: "329"
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    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "330"
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    state: "proved"
    last_update: "2026-05-11"
  formal_status:
    state: "Lean"
    last_update: "2026-05-11"
  status:
    state: "proved (Lean)"
    last_update: "2026-05-11"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-10-11"
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- number: "331"
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    state: "disproved"
    last_update: "2026-01-31"
  formal_status:
    state: "Lean"
    last_update: "2026-01-31"
  status:
    state: "disproved (Lean)"
    last_update: "2026-01-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-01-20"
  tags: ["number theory", "additive combinatorics"]

- number: "332"
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    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-11-25"
  tags: ["number theory"]

- number: "333"
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    state: "disproved"
    last_update: "2025-12-25"
  formal_status:
    state: "Lean"
    last_update: "2025-12-25"
  status:
    state: "disproved (Lean)"
    last_update: "2025-12-25"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-08-03"
  tags: ["number theory", "additive basis"]

- number: "334"
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    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A062241", "A045535"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "335"
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  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory", "additive combinatorics"]

- number: "336"
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    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory", "additive basis"]

- number: "337"
  prize: "no"
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    state: "disproved"
    last_update: "2025-12-10"
  formal_status:
    state: "Lean"
    last_update: "2025-12-10"
  status:
    state: "disproved (Lean)"
    last_update: "2025-12-10"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-08-03"
  tags: ["number theory", "additive combinatorics", "additive basis"]

- number: "338"
  prize: "no"
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    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory", "additive basis"]

- number: "339"
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    state: "proved"
    last_update: "2025-10-12"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-10-12"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory", "additive basis"]

- number: "340"
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    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A080200", "A005282"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["number theory", "additive combinatorics", "sidon sets"]

- number: "341"
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    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-01-22"
  tags: ["number theory"]

- number: "342"
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    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
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    last_update: "2025-08-31"
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    state: "yes"
    last_update: "2026-03-17"
  tags: ["number theory"]

- number: "343"
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    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
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- number: "344"
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    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
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- number: "345"
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    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
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    last_update: "2025-08-31"
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    state: "no"
    last_update: "2025-08-31"
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- number: "346"
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    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-01-04"
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- number: "347"
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    state: "proved"
    last_update: "2026-01-21"
  formal_status:
    state: "Lean"
    last_update: "2026-01-21"
  status:
    state: "proved (Lean)"
    last_update: "2026-01-21"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["number theory", "complete sequences"]

- number: "348"
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    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["number theory", "complete sequences"]

- number: "349"
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    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["number theory", "complete sequences"]

- number: "350"
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    state: "proved"
    last_update: "2025-11-25"
  formal_status:
    state: "Lean"
    last_update: "2025-11-25"
  status:
    state: "proved (Lean)"
    last_update: "2025-11-25"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["number theory", "additive combinatorics"]

- number: "351"
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    state: "proved"
    last_update: "2026-05-12"
  formal_status:
    state: "Lean"
    last_update: "2026-05-12"
  status:
    state: "proved (Lean)"
    last_update: "2026-05-12"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-10-14"
  tags: ["number theory", "complete sequences"]

- number: "352"
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    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["geometry"]

- number: "353"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2026-06-21"
  formal_status:
    state: "Lean"
    last_update: "2026-06-21"
  status:
    state: "proved (Lean)"
    last_update: "2026-06-21"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-07-22"
  tags: ["geometry"]

- number: "354"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-09-05"
  tags: ["number theory"]

- number: "355"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2026-02-02"
  formal_status:
    state: "Lean"
    last_update: "2026-02-02"
  status:
    state: "proved (Lean)"
    last_update: "2026-02-02"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-09-01"
  tags: ["number theory", "unit fractions"]

- number: "356"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "357"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A364132", "A364153", "possible"]
  formalized:
    state: "yes"
    last_update: "2025-10-17"
  tags: ["number theory"]

- number: "358"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2026-04-01"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2026-04-01"
  oeis: ["possible"]
  formalized:
    state: "yes"
    last_update: "2025-09-03"
  tags: ["number theory", "additive basis", "primes"]

- number: "359"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A002048"]
  formalized:
    state: "yes"
    last_update: "2025-11-28"
  comments: "segmented numbers"
  tags: ["number theory"]

- number: "360"
  prize: "no"
  informal_status:
    state: "solved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "solved"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "361"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "yes"
    last_update: "2025-09-05"
  tags: ["number theory"]

- number: "362"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "363"
  prize: "no"
  informal_status:
    state: "disproved"
    last_update: "2026-03-10"
  formal_status:
    state: "Lean"
    last_update: "2026-03-10"
  status:
    state: "disproved (Lean)"
    last_update: "2026-03-10"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-07-02"
  tags: ["number theory"]

- number: "364"
  prize: "no"
  informal_status:
    state: "verifiable"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "verifiable"
    last_update: "2025-08-31"
  oeis: ["A060355", "A076445"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "365"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-09-20"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-09-20"
  oeis: ["A060355", "A060859", "A175155"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "366"
  prize: "no"
  informal_status:
    state: "verifiable"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "verifiable"
    last_update: "2025-08-31"
  oeis: ["A060355"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "367"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A057521"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "368"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A074399"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "369"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2026-03-27"
  formal_status:
    state: "Lean"
    last_update: "2026-03-27"
  status:
    state: "proved (Lean)"
    last_update: "2026-03-27"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-08-03"
  tags: ["number theory"]

- number: "370"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-11-24"
  formal_status:
    state: "Lean"
    last_update: "2025-11-24"
  status:
    state: "proved (Lean)"
    last_update: "2025-11-24"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "371"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A070089"]
  formalized:
    state: "yes"
    last_update: "2025-10-21"
  tags: ["number theory"]

- number: "372"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["A071870"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "373"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A003135"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["number theory", "factorials"]

- number: "374"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A388851", "A387184", "A389117", "A389148"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "375"
  prize: "no"
  informal_status:
    state: "falsifiable"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "falsifiable"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-01-18"
  tags: ["number theory"]

- number: "376"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A030979"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["number theory", "binomial coefficients", "base representations"]

- number: "377"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["number theory", "binomial coefficients"]

- number: "378"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory", "binomial coefficients"]

- number: "379"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "Lean"
    last_update: "2025-08-31"
  status:
    state: "proved (Lean)"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["number theory", "binomial coefficients"]

- number: "380"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2026-03-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2026-03-31"
  oeis: ["A070003", "A388654", "A387054", "A389100"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "381"
  prize: "no"
  informal_status:
    state: "disproved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "disproved"
    last_update: "2025-08-31"
  oeis: ["A002182"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory", "divisors"]

- number: "382"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A388850"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "383"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "384"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory", "binomial coefficients"]

- number: "385"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A322292"]
  formalized:
    state: "yes"
    last_update: "2026-01-26"
  tags: ["number theory"]

- number: "386"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A280992"]
  formalized:
    state: "yes"
    last_update: "2026-01-11"
  tags: ["number theory", "binomial coefficients"]

- number: "387"
  prize: "no"
  informal_status:
    state: "solved"
    last_update: "2026-07-02"
  formal_status:
    state: "unformalized"
  status:
    state: "solved"
    last_update: "2026-07-02"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-01-02"
  tags: ["number theory", "binomial coefficients"]

- number: "388"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "389"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A375071"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "390"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A193429"]
  formalized:
    state: "yes"
    last_update: "2026-01-03"
  tags: ["number theory", "factorials"]

- number: "391"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["A034258", "A034259"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory", "factorials"]

- number: "392"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2026-02-22"
  formal_status:
    state: "Lean"
    last_update: "2026-02-22"
  status:
    state: "proved (Lean)"
    last_update: "2026-02-22"
  oeis: ["possible"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["number theory", "factorials"]

- number: "393"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A388302"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory", "factorials"]

- number: "394"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-10-28"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-10-28"
  oeis: ["A344005"]
  formalized:
    state: "yes"
    last_update: "2026-02-09"
  tags: ["number theory"]

- number: "395"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  comments: "reverse Littlewood-Offord problem"
  tags: ["analysis"]

- number: "396"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A375077"]
  formalized:
    state: "yes"
    last_update: "2025-11-27"
  tags: ["number theory", "binomial coefficients"]

- number: "397"
  prize: "no"
  informal_status:
    state: "disproved"
    last_update: "2026-01-10"
  formal_status:
    state: "Lean"
    last_update: "2026-01-10"
  status:
    state: "disproved (Lean)"
    last_update: "2026-01-10"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-11-21"
  tags: ["number theory", "binomial coefficients"]

- number: "398"
  prize: "no"
  informal_status:
    state: "falsifiable"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "falsifiable"
    last_update: "2025-08-31"
  oeis: ["A146968", "A141399"]
  formalized:
    state: "yes"
    last_update: "2025-09-01"
  comments: "Brocard-Ramanujan conjecture"
  tags: ["number theory", "factorials"]

- number: "399"
  prize: "no"
  informal_status:
    state: "disproved"
    last_update: "2026-02-04"
  formal_status:
    state: "Lean"
    last_update: "2026-02-04"
  status:
    state: "disproved (Lean)"
    last_update: "2026-02-04"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-01-12"
  tags: ["number theory", "factorials"]

- number: "400"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "yes"
    last_update: "2026-03-19"
  tags: ["number theory", "factorials"]

- number: "401"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2026-01-11"
  formal_status:
    state: "Lean"
    last_update: "2026-01-11"
  status:
    state: "proved (Lean)"
    last_update: "2026-01-11"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-08-03"
  tags: ["number theory", "factorials"]

- number: "402"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "403"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2026-06-21"
  formal_status:
    state: "Lean"
    last_update: "2026-06-21"
  status:
    state: "proved (Lean)"
    last_update: "2026-06-21"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-07-22"
  tags: ["number theory", "factorials"]

- number: "404"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory", "factorials"]

- number: "405"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory", "factorials"]

- number: "406"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["number theory", "base representations"]

- number: "407"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["possible", "A387688"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "408"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A049108"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory", "iterated functions"]

- number: "409"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A039651", "A229487"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["number theory", "iterated functions"]

- number: "410"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A007497", "possible"]
  formalized:
    state: "yes"
    last_update: "2025-09-01"
  tags: ["number theory", "iterated functions"]

- number: "411"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A383044", "possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory", "iterated functions"]

- number: "412"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A007497", "A051572"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["number theory", "iterated functions"]

- number: "413"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A005236"]
  formalized:
    state: "yes"
    last_update: "2026-01-06"
  tags: ["number theory", "iterated functions"]

- number: "414"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A064491", "possible"]
  formalized:
    state: "yes"
    last_update: "2025-12-09"
  tags: ["number theory", "iterated functions"]

- number: "415"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "416"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A264810"]
  formalized:
    state: "yes"
    last_update: "2025-09-04"
  tags: ["number theory"]

- number: "417"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A264810", "A061070"]
  formalized:
    state: "yes"
    last_update: "2026-01-22"
  tags: ["number theory"]

- number: "418"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-11-23"
  formal_status:
    state: "Lean"
    last_update: "2025-11-23"
  status:
    state: "proved (Lean)"
    last_update: "2025-11-23"
  oeis: ["A005278", "A263958"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "419"
  prize: "no"
  informal_status:
    state: "solved"
    last_update: "2026-01-31"
  formal_status:
    state: "Lean"
    last_update: "2026-01-31"
  status:
    state: "solved (Lean)"
    last_update: "2026-01-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-07-06"
  tags: ["number theory", "factorials"]

- number: "420"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "421"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A389544", "A390848"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "422"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A005185"]
  formalized:
    state: "yes"
    last_update: "2025-11-11"
  tags: ["number theory"]

- number: "423"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A005243"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "424"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A005244"]
  formalized:
    state: "yes"
    last_update: "2025-11-13"
  tags: ["number theory"]

- number: "425"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory", "sidon sets"]

- number: "426"
  prize: "$25"
  informal_status:
    state: "disproved"
    last_update: "2026-04-20"
  formal_status:
    state: "Lean"
    last_update: "2026-04-20"
  status:
    state: "disproved (Lean)"
    last_update: "2026-04-20"
  oeis: ["possible"]
  formalized:
    state: "yes"
    last_update: "2026-07-22"
  tags: ["graph theory"]

- number: "427"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2026-04-26"
  formal_status:
    state: "Lean"
    last_update: "2026-04-26"
  status:
    state: "proved (Lean)"
    last_update: "2026-04-26"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["number theory", "primes"]

- number: "428"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-01-07"
  tags: ["number theory", "primes"]

- number: "429"
  prize: "no"
  informal_status:
    state: "disproved"
    last_update: "2026-01-29"
  formal_status:
    state: "Lean"
    last_update: "2026-01-29"
  status:
    state: "disproved (Lean)"
    last_update: "2026-01-29"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-08-03"
  tags: ["number theory"]

- number: "430"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "431"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  comments: "inverse Goldbach problem"
  tags: ["number theory", "primes"]

- number: "432"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "433"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2026-02-24"
  formal_status:
    state: "Lean"
    last_update: "2026-02-24"
  status:
    state: "proved (Lean)"
    last_update: "2026-02-24"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "434"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2026-02-24"
  formal_status:
    state: "Lean"
    last_update: "2026-02-24"
  status:
    state: "proved (Lean)"
    last_update: "2026-02-24"
  oeis: ["possible"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "435"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2026-02-04"
  formal_status:
    state: "Lean"
    last_update: "2026-02-04"
  status:
    state: "proved (Lean)"
    last_update: "2026-02-04"
  oeis: ["A389479"]
  formalized:
    state: "yes"
    last_update: "2026-08-03"
  tags: ["number theory"]

- number: "436"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A000445", "possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "437"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "438"
  prize: "no"
  informal_status:
    state: "solved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "solved"
    last_update: "2025-08-31"
  oeis: ["A363069"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "439"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory", "ramsey theory"]

- number: "440"
  prize: "no"
  informal_status:
    state: "solved"
    last_update: "2025-12-27"
  formal_status:
    state: "unformalized"
  status:
    state: "solved"
    last_update: "2025-12-27"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "441"
  prize: "no"
  informal_status:
    state: "disproved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "disproved"
    last_update: "2025-08-31"
  oeis: ["A068509"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "442"
  prize: "no"
  informal_status:
    state: "disproved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "disproved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "443"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2026-02-04"
  formal_status:
    state: "Lean"
    last_update: "2026-02-04"
  status:
    state: "proved (Lean)"
    last_update: "2026-02-04"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-08-03"
  tags: ["number theory"]

- number: "444"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory", "divisors"]

- number: "445"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-03-16"
  tags: ["number theory"]

- number: "446"
  prize: "no"
  informal_status:
    state: "solved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "solved"
    last_update: "2025-08-31"
  oeis: ["A074738"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory", "divisors"]

- number: "447"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2026-02-10"
  formal_status:
    state: "Lean"
    last_update: "2026-02-10"
  status:
    state: "proved (Lean)"
    last_update: "2026-02-10"
  oeis: ["possible"]
  formalized:
    state: "yes"
    last_update: "2026-08-04"
  tags: ["combinatorics"]

- number: "448"
  prize: "no"
  informal_status:
    state: "disproved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "disproved"
    last_update: "2025-08-31"
  oeis: ["A397433"]
  formalized:
    state: "yes"
    last_update: "2026-06-23"
  tags: ["number theory", "divisors"]

- number: "449"
  prize: "no"
  informal_status:
    state: "disproved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "disproved"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory", "divisors"]

- number: "450"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-08-07"
  tags: ["number theory", "divisors"]

- number: "451"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A386620"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "452"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "453"
  prize: "no"
  informal_status:
    state: "disproved"
    last_update: "2026-01-31"
  formal_status:
    state: "Lean"
    last_update: "2026-01-31"
  status:
    state: "disproved (Lean)"
    last_update: "2026-01-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-07-06"
  tags: ["number theory"]

- number: "454"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A389676", "A389677"]
  formalized:
    state: "yes"
    last_update: "2026-01-03"
  tags: ["number theory", "primes"]

- number: "455"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-01-03"
  tags: ["number theory"]

- number: "456"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A034694", "A061026", "possible"]
  formalized:
    state: "yes"
    last_update: "2026-06-07"
  tags: ["number theory"]

- number: "457"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2026-03-07"
  formal_status:
    state: "Lean"
    last_update: "2026-03-07"
  status:
    state: "proved (Lean)"
    last_update: "2026-03-07"
  oeis: ["A391668"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "458"
  prize: "no"
  informal_status:
    state: "falsifiable"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "falsifiable"
    last_update: "2025-08-31"
  oeis: ["A056604"]
  formalized:
    state: "yes"
    last_update: "2025-11-21"
  tags: ["number theory", "primes"]

- number: "459"
  prize: "no"
  informal_status:
    state: "solved"
    last_update: "2026-03-11"
  formal_status:
    state: "Lean"
    last_update: "2026-03-11"
  status:
    state: "solved (Lean)"
    last_update: "2026-03-11"
  oeis: ["A289280"]
  formalized:
    state: "yes"
    last_update: "2026-06-29"
  tags: ["number theory", "primes"]

- number: "460"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  comments: "ambiguous statement"
  tags: ["number theory"]

- number: "461"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory", "primes"]

- number: "462"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A032742", "possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory", "primes"]

- number: "463"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["number theory", "primes"]

- number: "464"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2026-06-21"
  formal_status:
    state: "Lean"
    last_update: "2026-06-21"
  status:
    state: "proved (Lean)"
    last_update: "2026-06-21"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-07-22"
  tags: ["number theory"]

- number: "465"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "466"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "467"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  comments: "ambiguous statement"
  tags: ["number theory"]

- number: "468"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A167485", "A387502", "A387503"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory", "divisors"]

- number: "469"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2026-07-21"
  formal_status:
    state: "Lean"
    last_update: "2026-07-21"
  status:
    state: "proved (Lean)"
    last_update: "2026-07-21"
  oeis: ["A006036", "A119425", "possible"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["number theory", "divisors"]

- number: "470"
  prize: "$10"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A006037", "A002975"]
  formalized:
    state: "yes"
    last_update: "2025-09-16"
  tags: ["number theory", "divisors"]

- number: "471"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "472"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A389713", "possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "473"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["A055265"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "474"
  prize: "$100"
  informal_status:
    state: "not provable"
    last_update: "2025-10-01"
  formal_status:
    state: "unformalized"
  status:
    state: "not provable"
    last_update: "2025-10-01"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["set theory", "ramsey theory"]

- number: "475"
  prize: "no"
  informal_status:
    state: "decidable"
    last_update: "2026-02-23"
  formal_status:
    state: "unformalized"
  status:
    state: "decidable"
    last_update: "2026-02-23"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory", "additive combinatorics"]

- number: "476"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-12-31"
  formal_status:
    state: "Lean"
    last_update: "2025-12-31"
  status:
    state: "proved (Lean)"
    last_update: "2025-12-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-07-06"
  tags: ["number theory", "additive combinatorics"]

- number: "477"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "478"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A210184"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory", "factorials"]

- number: "479"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A036236", "A015919", "A050259", "A015921", "A006521", "A006517", "A015940"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "480"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "481"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-12-01"
  formal_status:
    state: "Lean"
    last_update: "2025-12-01"
  status:
    state: "proved (Lean)"
    last_update: "2025-12-01"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-08-04"
  tags: ["number theory"]

- number: "482"
  prize: "no"
  informal_status:
    state: "solved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "solved"
    last_update: "2025-08-31"
  oeis: ["A004539"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "483"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A030126"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory", "additive combinatorics", "ramsey theory"]

- number: "484"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2026-04-15"
  formal_status:
    state: "Lean"
    last_update: "2026-04-15"
  status:
    state: "proved (Lean)"
    last_update: "2026-04-15"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-08-03"
  tags: ["number theory", "additive combinatorics", "ramsey theory"]

- number: "485"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["analysis", "polynomials"]

- number: "486"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-12-29"
  tags: ["number theory", "primitive sets"]

- number: "487"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2026-02-16"
  formal_status:
    state: "Lean"
    last_update: "2026-02-16"
  status:
    state: "proved (Lean)"
    last_update: "2026-02-16"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-08-03"
  tags: ["number theory"]

- number: "488"
  prize: "no"
  informal_status:
    state: "falsifiable"
    last_update: "2026-03-29"
  formal_status:
    state: "unformalized"
  status:
    state: "falsifiable"
    last_update: "2026-03-29"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "489"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-02-13"
  tags: ["number theory"]

- number: "490"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2026-05-22"
  formal_status:
    state: "Lean"
    last_update: "2026-05-22"
  status:
    state: "proved (Lean)"
    last_update: "2026-05-22"
  oeis: ["A397205"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "491"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "492"
  prize: "no"
  informal_status:
    state: "disproved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "disproved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "493"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-12-27"
  formal_status:
    state: "Lean"
    last_update: "2025-12-27"
  status:
    state: "proved (Lean)"
    last_update: "2025-12-27"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-06-26"
  tags: ["number theory"]

- number: "494"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-10-14"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-10-14"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-12-30"
  tags: ["analysis", "additive combinatorics"]

- number: "495"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-01-07"
  comments: "Littlewood conjecture"
  tags: ["diophantine approximation", "number theory"]

- number: "496"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory", "diophantine approximation"]

- number: "497"
  prize: "no"
  informal_status:
    state: "solved"
    last_update: "2026-02-04"
  formal_status:
    state: "Lean"
    last_update: "2026-02-04"
  status:
    state: "solved (Lean)"
    last_update: "2026-02-04"
  oeis: ["A000372"]
  formalized:
    state: "yes"
    last_update: "2026-08-03"
  comments: "Dedekind's problem"
  tags: ["combinatorics"]

- number: "498"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2026-01-27"
  formal_status:
    state: "Lean"
    last_update: "2026-01-27"
  status:
    state: "proved (Lean)"
    last_update: "2026-01-27"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-08-03"
  comments: "strong Littlewood-Offord problem"
  tags: ["combinatorics", "analysis"]

- number: "499"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-11-29"
  formal_status:
    state: "Lean"
    last_update: "2025-11-29"
  status:
    state: "proved (Lean)"
    last_update: "2025-11-29"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["combinatorics"]

- number: "500"
  prize: "$500"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A140462"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory", "hypergraphs", "turan number"]

- number: "501"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-05-11"
  tags: ["combinatorics", "set theory"]

- number: "502"
  prize: "no"
  informal_status:
    state: "solved"
    last_update: "2026-02-02"
  formal_status:
    state: "Lean"
    last_update: "2026-02-02"
  status:
    state: "solved (Lean)"
    last_update: "2026-02-02"
  oeis: ["A027627"]
  formalized:
    state: "yes"
    last_update: "2026-08-03"
  tags: ["geometry", "distances"]

- number: "503"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A175769"]
  formalized:
    state: "yes"
    last_update: "2025-10-21"
  tags: ["geometry", "distances"]

- number: "504"
  prize: "no"
  informal_status:
    state: "solved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "solved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  comments: "Blumenthal's problem"
  tags: ["geometry"]

- number: "505"
  prize: "no"
  informal_status:
    state: "disproved"
    last_update: "2026-02-02"
  formal_status:
    state: "Lean"
    last_update: "2026-02-02"
  status:
    state: "disproved (Lean)"
    last_update: "2026-02-02"
  oeis: ["possible"]
  formalized:
    state: "yes"
    last_update: "2026-05-13"
  comments: "Borsuk's problem"
  tags: ["geometry"]

- number: "506"
  prize: "no"
  informal_status:
    state: "decidable"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "decidable"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "yes"
    last_update: "2026-08-14"
  tags: ["geometry"]

- number: "507"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-02-10"
  comments: "Heilbronn's triangle problem"
  tags: ["geometry"]

- number: "508"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-12-09"
  comments: "Hadwiger-Nelson problem"
  tags: ["geometry", "ramsey theory"]

- number: "509"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["analysis"]

- number: "510"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-11-12"
  comments: "Chowla's cosine problem"
  tags: ["analysis"]

- number: "511"
  prize: "no"
  informal_status:
    state: "disproved"
    last_update: "2025-09-15"
  formal_status:
    state: "unformalized"
  status:
    state: "disproved"
    last_update: "2025-09-15"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["analysis"]

- number: "512"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2026-06-22"
  formal_status:
    state: "Lean"
    last_update: "2026-06-22"
  status:
    state: "proved (Lean)"
    last_update: "2026-06-22"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-07-22"
  comments: "Littlewood's conjecture"
  tags: ["analysis"]

- number: "513"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-01-01"
  tags: ["analysis"]

- number: "514"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["analysis"]

- number: "515"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-10-19"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-10-19"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["analysis"]

- number: "516"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-12-28"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-12-28"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-01-01"
  tags: ["analysis"]

- number: "517"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-12-29"
  tags: ["analysis"]

- number: "518"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory", "ramsey theory"]

- number: "519"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2026-04-19"
  formal_status:
    state: "Lean"
    last_update: "2026-04-19"
  status:
    state: "proved (Lean)"
    last_update: "2026-04-19"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-07-06"
  tags: ["analysis"]

- number: "520"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-12-20"
  tags: ["number theory", "probability"]

- number: "521"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-08-07"
  tags: ["analysis", "polynomials", "probability"]

- number: "522"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-12-08"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-12-08"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["analysis", "polynomials", "probability"]

- number: "523"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["analysis", "probability", "polynomials"]

- number: "524"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["analysis", "probability", "polynomials"]

- number: "525"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["analysis", "probability", "polynomials"]

- number: "526"
  prize: "no"
  informal_status:
    state: "solved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "solved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["probability", "geometry"]

- number: "527"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-09-08"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-09-08"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["analysis", "probability"]

- number: "528"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A387897", "A156816"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["geometry"]

- number: "529"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["geometry", "probability"]

- number: "530"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A143824", "possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory", "sidon sets"]

- number: "531"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory", "ramsey theory"]

- number: "532"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2026-01-31"
  formal_status:
    state: "Lean"
    last_update: "2026-01-31"
  status:
    state: "proved (Lean)"
    last_update: "2026-01-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-06-26"
  tags: ["number theory", "ramsey theory"]

- number: "533"
  prize: "no"
  informal_status:
    state: "disproved"
    last_update: "2026-01-26"
  formal_status:
    state: "unformalized"
  status:
    state: "disproved"
    last_update: "2026-01-26"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-07-02"
  tags: ["graph theory"]

- number: "534"
  prize: "no"
  informal_status:
    state: "solved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "solved"
    last_update: "2025-08-31"
  oeis: ["A387543", "A387698"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory", "intersecting family"]

- number: "535"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "yes"
    last_update: "2026-04-17"
  tags: ["number theory"]

- number: "536"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "yes"
    last_update: "2025-11-12"
  tags: ["number theory"]

- number: "537"
  prize: "no"
  informal_status:
    state: "disproved"
    last_update: "2026-02-06"
  formal_status:
    state: "Lean"
    last_update: "2026-02-06"
  status:
    state: "disproved (Lean)"
    last_update: "2026-02-06"
  oeis: ["possible"]
  formalized:
    state: "yes"
    last_update: "2026-08-03"
  tags: ["number theory"]

- number: "538"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-08-07"
  tags: ["number theory"]

- number: "539"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "yes"
    last_update: "2026-04-16"
  tags: ["number theory"]

- number: "540"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2026-04-15"
  formal_status:
    state: "Lean"
    last_update: "2026-04-15"
  status:
    state: "proved (Lean)"
    last_update: "2026-04-15"
  oeis: ["A034463"]
  formalized:
    state: "yes"
    last_update: "2026-07-06"
  tags: ["number theory"]

- number: "541"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-12-30"
  formal_status:
    state: "Lean"
    last_update: "2025-12-30"
  status:
    state: "proved (Lean)"
    last_update: "2025-12-30"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "542"
  prize: "no"
  informal_status:
    state: "solved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "solved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "543"
  prize: "no"
  informal_status:
    state: "disproved"
    last_update: "2026-01-23"
  formal_status:
    state: "unformalized"
  status:
    state: "disproved"
    last_update: "2026-01-23"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory", "group theory"]

- number: "544"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A000791"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory", "ramsey theory"]

- number: "545"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-12-02"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-12-02"
  oeis: ["A059442", "possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory", "ramsey theory"]

- number: "546"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory", "ramsey theory"]

- number: "547"
  prize: "no"
  informal_status:
    state: "decidable"
    last_update: "2025-09-11"
  formal_status:
    state: "unformalized"
  status:
    state: "decidable"
    last_update: "2025-09-11"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory", "ramsey theory"]

- number: "548"
  prize: "no"
  informal_status:
    state: "falsifiable"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "falsifiable"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory"]

- number: "549"
  prize: "no"
  informal_status:
    state: "disproved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "disproved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory", "ramsey theory"]

- number: "550"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory", "ramsey theory"]

- number: "551"
  prize: "no"
  informal_status:
    state: "decidable"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "decidable"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory", "ramsey theory"]

- number: "552"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A006672"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory", "ramsey theory"]

- number: "553"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["A000791", "possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory", "ramsey theory"]

- number: "554"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory", "ramsey theory"]

- number: "555"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A389313", "possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory", "ramsey theory"]

- number: "556"
  prize: "no"
  informal_status:
    state: "decidable"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "decidable"
    last_update: "2025-08-31"
  oeis: ["A389335"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory", "ramsey theory"]

- number: "557"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory", "ramsey theory"]

- number: "558"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory", "ramsey theory"]

- number: "559"
  prize: "no"
  informal_status:
    state: "disproved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "disproved"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory", "ramsey theory"]

- number: "560"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory", "ramsey theory"]

- number: "561"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory", "ramsey theory"]

- number: "562"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "yes"
    last_update: "2025-12-30"
  tags: ["graph theory", "ramsey theory", "hypergraphs"]

- number: "563"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory", "ramsey theory", "hypergraphs"]

- number: "564"
  prize: "$500"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "yes"
    last_update: "2026-01-07"
  tags: ["graph theory", "ramsey theory", "hypergraphs"]

- number: "565"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-09-29"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-09-29"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory", "ramsey theory"]

- number: "566"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-01-08"
  tags: ["graph theory", "ramsey theory"]

- number: "567"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-01-09"
  tags: ["graph theory", "ramsey theory"]

- number: "568"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory", "ramsey theory"]

- number: "569"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory", "ramsey theory"]

- number: "570"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2026-01-16"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2026-01-16"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory", "ramsey theory"]

- number: "571"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory", "turan number"]

- number: "572"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory", "turan number"]

- number: "573"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A006856"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory", "turan number"]

- number: "574"
  prize: "no"
  informal_status:
    state: "disproved"
    last_update: "2026-03-28"
  formal_status:
    state: "unformalized"
  status:
    state: "disproved"
    last_update: "2026-03-28"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory", "turan number"]

- number: "575"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory", "turan number"]

- number: "576"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory", "turan number"]

- number: "577"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory"]

- number: "578"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory"]

- number: "579"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-07-02"
  tags: ["graph theory", "turan number"]

- number: "580"
  prize: "no"
  informal_status:
    state: "decidable"
    last_update: "2025-10-23"
  formal_status:
    state: "unformalized"
  status:
    state: "decidable"
    last_update: "2025-10-23"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory"]

- number: "581"
  prize: "no"
  informal_status:
    state: "solved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "solved"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory"]

- number: "582"
  prize: "$100"
  informal_status:
    state: "proved"
    last_update: "2026-02-05"
  formal_status:
    state: "Lean"
    last_update: "2026-02-05"
  status:
    state: "proved (Lean)"
    last_update: "2026-02-05"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-08-03"
  tags: ["graph theory", "ramsey theory"]

- number: "583"
  prize: "no"
  informal_status:
    state: "falsifiable"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "falsifiable"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory"]

- number: "584"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory", "cycles"]

- number: "585"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory", "cycles"]

- number: "586"
  prize: "no"
  informal_status:
    state: "disproved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "disproved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory", "covering systems"]

- number: "587"
  prize: "no"
  informal_status:
    state: "solved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "solved"
    last_update: "2025-08-31"
  oeis: ["A372040"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "588"
  prize: "$100"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A006065", "A008997"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["geometry"]

- number: "589"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["geometry"]

- number: "590"
  prize: "$250"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["set theory", "ramsey theory"]

- number: "591"
  prize: "$250"
  informal_status:
    state: "proved"
    last_update: "2026-01-17"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2026-01-17"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["set theory", "ramsey theory"]

- number: "592"
  prize: "$1000"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["set theory", "ramsey theory"]

- number: "593"
  prize: "$500"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-05-21"
  tags: ["set theory", "graph theory", "hypergraphs", "chromatic number"]

- number: "594"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-06-21"
  tags: ["graph theory", "set theory"]

- number: "595"
  prize: "$250"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-05-11"
  tags: ["graph theory", "set theory"]

- number: "596"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
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  status:
    state: "open"
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    state: "yes"
    last_update: "2026-05-30"
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- number: "597"
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    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
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    state: "no"
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- number: "598"
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    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
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  oeis: ["N/A"]
  formalized:
    state: "yes"
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  tags: ["set theory", "ramsey theory"]

- number: "599"
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    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-06-22"
  comments: "Erdős-Menger conjecture"
  tags: ["graph theory", "set theory"]

- number: "600"
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    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "yes"
    last_update: "2026-07-16"
  tags: ["graph theory"]

- number: "601"
  prize: "$500"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory", "set theory"]

- number: "602"
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    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
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    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-04-16"
  comments: "Property B"
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- number: "603"
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    state: "solved"
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  formal_status:
    state: "unformalized"
  status:
    state: "solved"
    last_update: "2026-07-06"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["combinatorics", "set theory"]

- number: "604"
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    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  comments: "pinned distance problem"
  tags: ["geometry", "distances"]

- number: "605"
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    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["possible"]
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    state: "no"
    last_update: "2025-08-31"
  tags: ["geometry", "distances"]

- number: "606"
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    state: "solved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "solved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["geometry"]

- number: "607"
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    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["geometry"]

- number: "608"
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    state: "disproved"
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  formal_status:
    state: "Lean"
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    url: "https://github.com/primateria/erdos608"
  status:
    state: "disproved (Lean)"
    last_update: "2026-07-29"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
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- number: "609"
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    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory", "ramsey theory"]

- number: "610"
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    state: "proved"
    last_update: "2026-06-07"
  formal_status:
    state: "Lean"
    last_update: "2026-06-07"
  status:
    state: "proved (Lean)"
    last_update: "2026-06-07"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory"]

- number: "611"
  prize: "no"
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    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory"]

- number: "612"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory"]

- number: "613"
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    state: "disproved"
    last_update: "2025-11-04"
  formal_status:
    state: "Lean"
    last_update: "2025-11-04"
  status:
    state: "disproved (Lean)"
    last_update: "2025-11-04"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-05-09"
  tags: ["graph theory"]

- number: "614"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory"]

- number: "615"
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    state: "disproved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "disproved"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "yes"
    last_update: "2026-06-20"
  tags: ["graph theory", "ramsey theory"]

- number: "616"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory"]

- number: "617"
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    state: "falsifiable"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "falsifiable"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-01-24"
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- number: "618"
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    state: "proved"
    last_update: "2026-02-08"
  formal_status:
    state: "Lean"
    last_update: "2026-02-08"
  status:
    state: "proved (Lean)"
    last_update: "2026-02-08"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-08-03"
  tags: ["graph theory"]

- number: "619"
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    state: "solved"
    last_update: "2026-06-22"
  formal_status:
    state: "Lean"
    last_update: "2026-06-22"
  status:
    state: "solved (Lean)"
    last_update: "2026-06-22"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-06-13"
  tags: ["graph theory"]

- number: "620"
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    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
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  formalized:
    state: "no"
    last_update: "2025-08-31"
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  tags: ["graph theory"]

- number: "621"
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    state: "proved"
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  formal_status:
    state: "Lean"
    last_update: "2026-04-19"
  status:
    state: "proved (Lean)"
    last_update: "2026-04-19"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-07-22"
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- number: "622"
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    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory"]

- number: "623"
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    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
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    state: "yes"
    last_update: "2025-11-12"
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- number: "624"
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    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "yes"
    last_update: "2025-11-13"
  tags: ["combinatorics"]

- number: "625"
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    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
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- number: "626"
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    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
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    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
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- number: "627"
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    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
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  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory", "chromatic number"]

- number: "628"
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    state: "falsifiable"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
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    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-08-03"
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  tags: ["graph theory", "chromatic number"]

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  prize: "no"
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    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory", "chromatic number"]

- number: "630"
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    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
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    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
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    state: "no"
    last_update: "2025-08-31"
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    state: "disproved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "disproved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
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    last_update: "2026-04-06"
  formal_status:
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  status:
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    state: "open"
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  formal_status:
    state: "unformalized"
  status:
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  oeis: ["possible"]
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  formal_status:
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  status:
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  oeis: ["N/A"]
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    state: "no"
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- number: "636"
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  status:
    state: "proved"
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  oeis: ["N/A"]
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  tags: ["graph theory", "ramsey theory"]

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    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
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    state: "no"
    last_update: "2025-08-31"
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    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory", "ramsey theory"]

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    state: "proved"
    last_update: "2026-05-06"
  formal_status:
    state: "Lean"
    last_update: "2026-05-06"
  status:
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    last_update: "2026-05-06"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-07-22"
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- number: "640"
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    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory", "chromatic number"]

- number: "641"
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    state: "disproved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "disproved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory"]

- number: "642"
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    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["possible"]
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    state: "no"
    last_update: "2025-08-31"
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- number: "643"
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    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
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  formalized:
    state: "no"
    last_update: "2025-08-31"
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- number: "644"
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    state: "open"
    last_update: "2025-08-31"
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    state: "open"
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    state: "no"
    last_update: "2025-08-31"
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- number: "645"
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    state: "proved"
    last_update: "2025-11-23"
  formal_status:
    state: "Lean"
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  status:
    state: "proved (Lean)"
    last_update: "2025-11-23"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
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- number: "646"
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    state: "proved"
    last_update: "2026-03-02"
  formal_status:
    state: "Lean"
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  status:
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    last_update: "2026-03-02"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-08-03"
  tags: ["number theory", "factorials"]

- number: "647"
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    state: "verifiable"
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  status:
    state: "verifiable"
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  oeis: ["A062249", "A087280"]
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    state: "yes"
    last_update: "2025-10-13"
  tags: ["number theory"]

- number: "648"
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    state: "solved"
    last_update: "2026-02-04"
  formal_status:
    state: "Lean"
    last_update: "2026-02-04"
  status:
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    last_update: "2026-02-04"
  oeis: ["A391750"]
  formalized:
    state: "yes"
    last_update: "2026-07-22"
  tags: ["number theory"]

- number: "649"
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    state: "disproved"
    last_update: "2026-02-07"
  formal_status:
    state: "Lean"
    last_update: "2026-02-07"
  status:
    state: "disproved (Lean)"
    last_update: "2026-02-07"
  oeis: ["possible"]
  formalized:
    state: "yes"
    last_update: "2026-08-04"
  tags: ["number theory"]

- number: "650"
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    state: "solved"
    last_update: "2026-03-06"
  formal_status:
    state: "Lean"
    last_update: "2026-03-06"
  status:
    state: "solved (Lean)"
    last_update: "2026-03-06"
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  formalized:
    state: "yes"
    last_update: "2026-08-04"
  tags: ["number theory"]

- number: "651"
  prize: "no"
  informal_status:
    state: "disproved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "disproved"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["geometry", "convex"]

- number: "652"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2026-01-17"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2026-01-17"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["geometry", "distances"]

- number: "653"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "yes"
    last_update: "2026-04-16"
  tags: ["geometry", "distances"]

- number: "654"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["geometry", "distances"]

- number: "655"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "yes"
    last_update: "2026-04-16"
  comments: "ambiguous statement"
  tags: ["geometry", "distances"]

- number: "656"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory", "additive combinatorics"]

- number: "657"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["geometry", "distances"]

- number: "658"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2026-04-20"
  formal_status:
    state: "Lean"
    last_update: "2026-04-20"
  status:
    state: "proved (Lean)"
    last_update: "2026-04-20"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["additive combinatorics"]

- number: "659"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2026-01-14"
  formal_status:
    state: "Lean"
    last_update: "2026-01-14"
  status:
    state: "proved (Lean)"
    last_update: "2026-01-14"
  oeis: ["possible"]
  formalized:
    state: "yes"
    last_update: "2025-11-12"
  tags: ["geometry", "distances"]

- number: "660"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "yes"
    last_update: "2026-08-09"
  comments: "ambiguous statement"
  tags: ["geometry", "distances", "convex"]

- number: "661"
  prize: "$50"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["geometry", "distances"]

- number: "662"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  comments: "ambiguous statement"
  tags: ["geometry", "distances"]

- number: "663"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A391668"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "664"
  prize: "no"
  informal_status:
    state: "disproved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "disproved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["combinatorics"]

- number: "665"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["combinatorics"]

- number: "666"
  prize: "no"
  informal_status:
    state: "disproved"
    last_update: "2026-02-06"
  formal_status:
    state: "Lean"
    last_update: "2026-02-06"
  status:
    state: "disproved (Lean)"
    last_update: "2026-02-06"
  oeis: ["possible"]
  formalized:
    state: "yes"
    last_update: "2026-08-04"
  tags: ["graph theory"]

- number: "667"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory", "ramsey theory"]

- number: "668"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A385657"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["geometry", "distances"]

- number: "669"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A003035", "A006065", "A008997", "possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  comments: "orchard problems"
  tags: ["geometry"]

- number: "670"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2026-04-16"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2026-04-16"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["geometry", "distances"]

- number: "671"
  prize: "$250"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["analysis"]

- number: "672"
  prize: "no"
  informal_status:
    state: "verifiable"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "verifiable"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "673"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory", "divisors"]

- number: "674"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-12-08"
  formal_status:
    state: "Lean"
    last_update: "2025-12-08"
  status:
    state: "proved (Lean)"
    last_update: "2025-12-08"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-08-03"
  tags: ["number theory"]

- number: "675"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "676"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A390181", "in progress"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "677"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "yes"
    last_update: "2025-12-02"
  tags: ["number theory"]

- number: "678"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2026-01-07"
  formal_status:
    state: "Lean"
    last_update: "2026-01-07"
  status:
    state: "proved (Lean)"
    last_update: "2026-01-07"
  oeis: ["possible"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "679"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "680"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-11-21"
  tags: ["number theory", "primes"]

- number: "681"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A389680"]
  formalized:
    state: "yes"
    last_update: "2025-12-07"
  tags: ["number theory", "primes"]

- number: "682"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["A386978"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory", "primes"]

- number: "683"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-09-04"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-09-04"
  oeis: ["A006530", "A074399", "A121359", "possible"]
  formalized:
    state: "yes"
    last_update: "2026-03-12"
  tags: ["number theory", "primes", "binomial coefficients"]

- number: "684"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A392019", "possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory", "primes", "binomial coefficients"]

- number: "685"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory", "primes", "binomial coefficients"]

- number: "686"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-10-13"
  tags: ["number theory"]

- number: "687"
  prize: "$1000"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A048670", "A058989"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "688"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-05-11"
  tags: ["number theory"]

- number: "689"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "690"
  prize: "no"
  informal_status:
    state: "solved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "solved"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "691"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "692"
  prize: "no"
  informal_status:
    state: "disproved"
    last_update: "2026-04-02"
  formal_status:
    state: "Lean"
    last_update: "2026-04-02"
  status:
    state: "disproved (Lean)"
    last_update: "2026-04-02"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-08-04"
  tags: ["number theory", "divisors"]

- number: "693"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A391118", "possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory", "divisors"]

- number: "694"
  prize: "no"
  informal_status:
    state: "solved"
    last_update: "2026-05-06"
  formal_status:
    state: "Lean"
    last_update: "2026-05-06"
  status:
    state: "solved (Lean)"
    last_update: "2026-05-06"
  oeis: ["possible"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "695"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A061092"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "696"
  prize: "no"
  informal_status:
    state: "solved"
    last_update: "2026-05-11"
  formal_status:
    state: "Lean"
    last_update: "2026-05-11"
  status:
    state: "solved (Lean)"
    last_update: "2026-05-11"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory", "divisors"]

- number: "697"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-12-20"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-12-20"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-01-14"
  tags: ["number theory", "divisors"]

- number: "698"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2026-01-16"
  formal_status:
    state: "Lean"
    last_update: "2026-01-16"
  status:
    state: "proved (Lean)"
    last_update: "2026-01-16"
  oeis: ["possible"]
  formalized:
    state: "yes"
    last_update: "2026-08-04"
  tags: ["number theory", "binomial coefficients"]

- number: "699"
  prize: "no"
  informal_status:
    state: "falsifiable"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "falsifiable"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-01-04"
  tags: ["number theory", "binomial coefficients"]

- number: "700"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A091963", "possible"]
  formalized:
    state: "yes"
    last_update: "2026-06-24"
  tags: ["number theory", "binomial coefficients"]

- number: "701"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-04-20"
  tags: ["combinatorics", "intersecting family"]

- number: "702"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["combinatorics"]

- number: "703"
  prize: "$250"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["A390645"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["combinatorics"]

- number: "704"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory", "geometry", "chromatic number"]

- number: "705"
  prize: "no"
  informal_status:
    state: "disproved"
    last_update: "2026-01-27"
  formal_status:
    state: "unformalized"
  status:
    state: "disproved"
    last_update: "2026-01-27"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-11-27"
  tags: ["graph theory", "chromatic number"]

- number: "706"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory", "chromatic number"]

- number: "707"
  prize: "$1000"
  informal_status:
    state: "disproved"
    last_update: "2025-10-21"
  formal_status:
    state: "Lean"
    last_update: "2025-10-21"
  status:
    state: "disproved (Lean)"
    last_update: "2025-10-21"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["additive combinatorics", "sidon sets"]

- number: "708"
  prize: "$100"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "709"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "710"
  prize: "₹2000"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A390246"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "711"
  prize: "₹1000"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "712"
  prize: "$500"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory", "turan number", "hypergraphs"]

- number: "713"
  prize: "$500"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory", "turan number"]

- number: "714"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory", "turan number"]

- number: "715"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory"]

- number: "716"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2026-06-21"
  formal_status:
    state: "Lean"
    last_update: "2026-06-21"
  status:
    state: "proved (Lean)"
    last_update: "2026-06-21"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  comments: "Ruzsa-Szemerédi problem"
  tags: ["graph theory", "hypergraphs"]

- number: "717"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory"]

- number: "718"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory"]

- number: "719"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory", "hypergraphs"]

- number: "720"
  prize: "$100"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory", "ramsey theory"]

- number: "721"
  prize: "no"
  informal_status:
    state: "solved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "solved"
    last_update: "2025-08-31"
  oeis: ["A171081"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory", "additive combinatorics", "ramsey theory"]

- number: "722"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["combinatorics"]

- number: "723"
  prize: "no"
  informal_status:
    state: "falsifiable"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "falsifiable"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["combinatorics"]

- number: "724"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A001438"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["combinatorics"]

- number: "725"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A001009"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["combinatorics"]

- number: "726"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-06-25"
  tags: ["number theory"]

- number: "727"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A002503", "A343507", "A389396"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["number theory", "factorials"]

- number: "728"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2026-01-05"
  formal_status:
    state: "Lean"
    last_update: "2026-01-05"
  status:
    state: "proved (Lean)"
    last_update: "2026-01-05"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-10-14"
  tags: ["number theory", "factorials"]

- number: "729"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2026-01-10"
  formal_status:
    state: "Lean"
    last_update: "2026-01-10"
  status:
    state: "proved (Lean)"
    last_update: "2026-01-10"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-06-26"
  tags: ["number theory", "factorials"]

- number: "730"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A129515"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["number theory", "binomial coefficients", "base representations"]

- number: "731"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A006197"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory", "binomial coefficients"]

- number: "732"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["combinatorics"]

- number: "733"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["combinatorics", "geometry"]

- number: "734"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["combinatorics"]

- number: "735"
  prize: "no"
  informal_status:
    state: "solved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "solved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["geometry"]

- number: "736"
  prize: "no"
  informal_status:
    state: "not provable"
    last_update: "2025-10-01"
  formal_status:
    state: "unformalized"
  status:
    state: "not provable"
    last_update: "2025-10-01"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory", "chromatic number"]

- number: "737"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-10-01"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-10-01"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory", "chromatic number"]

- number: "738"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory", "chromatic number"]

- number: "739"
  prize: "no"
  informal_status:
    state: "not provable"
    last_update: "2025-10-01"
  formal_status:
    state: "unformalized"
  status:
    state: "not provable"
    last_update: "2025-10-01"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory", "chromatic number"]

- number: "740"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-05-09"
  tags: ["graph theory", "chromatic number"]

- number: "741"
  prize: "no"
  informal_status:
    state: "solved"
    last_update: "2025-08-31"
  formal_status:
    state: "Lean"
    last_update: "2025-08-31"
  status:
    state: "solved (Lean)"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-01-06"
  tags: ["additive combinatorics"]

- number: "742"
  prize: "no"
  informal_status:
    state: "decidable"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "decidable"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-06-29"
  tags: ["graph theory"]

- number: "743"
  prize: "no"
  informal_status:
    state: "falsifiable"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "falsifiable"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  comments: "tree packing conjecture"
  tags: ["graph theory"]

- number: "744"
  prize: "no"
  informal_status:
    state: "disproved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "disproved"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory", "chromatic number"]

- number: "745"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory"]

- number: "746"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory"]

- number: "747"
  prize: "no"
  informal_status:
    state: "solved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "solved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["combinatorics", "hypergraphs"]

- number: "748"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["A007865"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  comments: "Cameron-Erdős conjecture"
  tags: ["number theory"]

- number: "749"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-11-19"
  tags: ["additive combinatorics"]

- number: "750"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "Lean"
    last_update: "2025-08-31"
  status:
    state: "proved (Lean)"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-04-16"
  tags: ["graph theory", "chromatic number"]

- number: "751"
  prize: "no"
  informal_status:
    state: "disproved"
    last_update: "2026-01-27"
  formal_status:
    state: "Lean"
    last_update: "2026-01-27"
  status:
    state: "disproved (Lean)"
    last_update: "2026-01-27"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-08-04"
  tags: ["graph theory", "chromatic number"]

- number: "752"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory", "cycles"]

- number: "753"
  prize: "no"
  informal_status:
    state: "disproved"
    last_update: "2026-04-14"
  formal_status:
    state: "Lean"
    last_update: "2026-04-14"
  status:
    state: "disproved (Lean)"
    last_update: "2026-04-14"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-08-04"
  tags: ["graph theory", "chromatic number"]

- number: "754"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["geometry", "distances"]

- number: "755"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "yes"
    last_update: "2026-06-08"
  tags: ["geometry"]

- number: "756"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2026-03-15"
  formal_status:
    state: "Lean"
    last_update: "2026-03-15"
  status:
    state: "proved (Lean)"
    last_update: "2026-03-15"
  oeis: ["possible"]
  formalized:
    state: "yes"
    last_update: "2026-08-04"
  tags: ["geometry", "distances"]

- number: "757"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "yes"
    last_update: "2026-01-08"
  tags: ["geometry", "distances", "sidon sets"]

- number: "758"
  prize: "no"
  informal_status:
    state: "solved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "solved"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory", "chromatic number"]

- number: "759"
  prize: "no"
  informal_status:
    state: "solved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "solved"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory", "chromatic number"]

- number: "760"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2026-04-23"
  formal_status:
    state: "Lean"
    last_update: "2026-04-23"
  status:
    state: "proved (Lean)"
    last_update: "2026-04-23"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-08-04"
  tags: ["graph theory", "chromatic number"]

- number: "761"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory", "chromatic number"]

- number: "762"
  prize: "no"
  informal_status:
    state: "disproved"
    last_update: "2026-02-08"
  formal_status:
    state: "Lean"
    last_update: "2026-02-08"
  status:
    state: "disproved (Lean)"
    last_update: "2026-02-08"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-08-04"
  tags: ["graph theory", "chromatic number"]

- number: "763"
  prize: "no"
  informal_status:
    state: "disproved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "disproved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory", "additive combinatorics"]

- number: "764"
  prize: "no"
  informal_status:
    state: "disproved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "disproved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory", "additive combinatorics"]

- number: "765"
  prize: "no"
  informal_status:
    state: "solved"
    last_update: "2026-05-16"
  formal_status:
    state: "Lean"
    last_update: "2026-05-16"
  status:
    state: "solved (Lean)"
    last_update: "2026-05-16"
  oeis: ["A006855"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory", "turan number"]

- number: "766"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory", "turan number"]

- number: "767"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory", "turan number"]

- number: "768"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A001034", "A352287"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "769"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A014544", "possible"]
  formalized:
    state: "yes"
    last_update: "2026-08-07"
  tags: ["number theory", "geometry"]

- number: "770"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A263647", "possible"]
  formalized:
    state: "yes"
    last_update: "2026-01-20"
  tags: ["number theory"]

- number: "771"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "772"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory", "sidon sets", "additive combinatorics"]

- number: "773"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A390813"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory", "sidon sets", "squares"]

- number: "774"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-04-16"
  tags: ["number theory"]

- number: "775"
  prize: "no"
  informal_status:
    state: "disproved"
    last_update: "2026-04-19"
  formal_status:
    state: "Lean"
    last_update: "2026-04-19"
  status:
    state: "disproved (Lean)"
    last_update: "2026-04-19"
  oeis: ["possible"]
  formalized:
    state: "yes"
    last_update: "2026-08-04"
  tags: ["graph theory", "hypergraphs"]

- number: "776"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["combinatorics"]

- number: "777"
  prize: "no"
  informal_status:
    state: "solved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "solved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory", "combinatorics"]

- number: "778"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory"]

- number: "779"
  prize: "no"
  informal_status:
    state: "falsifiable"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "falsifiable"
    last_update: "2025-08-31"
  oeis: ["A005235"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["number theory", "primes"]

- number: "780"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["combinatorics", "hypergraphs", "chromatic number"]

- number: "781"
  prize: "no"
  informal_status:
    state: "disproved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "disproved"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["additive combinatorics"]

- number: "782"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "783"
  prize: "no"
  informal_status:
    state: "solved"
    last_update: "2026-04-19"
  formal_status:
    state: "unformalized"
  status:
    state: "solved"
    last_update: "2026-04-19"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "784"
  prize: "no"
  informal_status:
    state: "solved"
    last_update: "2025-12-20"
  formal_status:
    state: "unformalized"
  status:
    state: "solved"
    last_update: "2025-12-20"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "785"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2026-03-06"
  formal_status:
    state: "Lean"
    last_update: "2026-03-06"
  status:
    state: "proved (Lean)"
    last_update: "2026-03-06"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-08-04"
  comments: "exact additive complements"
  tags: ["additive combinatorics"]

- number: "786"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A143301", "possible"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "787"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["additive combinatorics"]

- number: "788"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["additive combinatorics"]

- number: "789"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "yes"
    last_update: "2026-04-16"
  tags: ["additive combinatorics"]

- number: "790"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["additive combinatorics"]

- number: "791"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A066063"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["additive combinatorics"]

- number: "792"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["additive combinatorics"]

- number: "793"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "Lean"
    last_update: "2025-08-31"
  status:
    state: "proved (Lean)"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "794"
  prize: "no"
  informal_status:
    state: "disproved"
    last_update: "2026-02-05"
  formal_status:
    state: "Lean"
    last_update: "2026-02-05"
  status:
    state: "disproved (Lean)"
    last_update: "2026-02-05"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-08-04"
  tags: ["graph theory", "hypergraphs", "turan number"]

- number: "795"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "796"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "yes"
    last_update: "2026-08-07"
  tags: ["number theory"]

- number: "797"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory", "chromatic number"]

- number: "798"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2026-05-08"
  formal_status:
    state: "Lean"
    last_update: "2026-05-08"
  status:
    state: "proved (Lean)"
    last_update: "2026-05-08"
  oeis: ["A116446"]
  formalized:
    state: "yes"
    last_update: "2026-08-04"
  tags: ["geometry"]

- number: "799"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory", "chromatic number"]

- number: "800"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory", "ramsey theory"]

- number: "801"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory", "ramsey theory"]

- number: "802"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory"]

- number: "803"
  prize: "no"
  informal_status:
    state: "disproved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "disproved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory"]

- number: "804"
  prize: "no"
  informal_status:
    state: "disproved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "disproved"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory"]

- number: "805"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory"]

- number: "806"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["additive combinatorics"]

- number: "807"
  prize: "no"
  informal_status:
    state: "disproved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "disproved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory"]

- number: "808"
  prize: "no"
  informal_status:
    state: "disproved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "disproved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["additive combinatorics", "graph theory"]

- number: "809"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory", "ramsey theory"]

- number: "810"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory", "ramsey theory"]

- number: "811"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory", "ramsey theory"]

- number: "812"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A059442"]
  formalized:
    state: "yes"
    last_update: "2026-03-08"
  tags: ["graph theory", "ramsey theory"]

- number: "813"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory"]

- number: "814"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory"]

- number: "815"
  prize: "no"
  informal_status:
    state: "disproved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "disproved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory"]

- number: "816"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory"]

- number: "817"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["additive combinatorics"]

- number: "818"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2026-04-25"
  formal_status:
    state: "Lean"
    last_update: "2026-04-25"
  status:
    state: "proved (Lean)"
    last_update: "2026-04-25"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-08-04"
  tags: ["additive combinatorics"]

- number: "819"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["additive combinatorics"]

- number: "820"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A263647"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "821"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A014197"]
  formalized:
    state: "yes"
    last_update: "2026-07-02"
  tags: ["number theory"]

- number: "822"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-10-14"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-10-14"
  oeis: ["A121048", "A155085"]
  formalized:
    state: "yes"
    last_update: "2025-12-10"
  tags: ["number theory"]

- number: "823"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "824"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "825"
  prize: "$25"
  informal_status:
    state: "proved"
    last_update: "2026-01-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2026-01-31"
  oeis: ["A006037", "A330244"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "826"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "827"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["geometry"]

- number: "828"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-09-01"
  tags: ["number theory"]

- number: "829"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "yes"
    last_update: "2026-06-07"
  tags: ["number theory"]

- number: "830"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A259180"]
  formalized:
    state: "yes"
    last_update: "2025-09-01"
  tags: ["number theory"]

- number: "831"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["geometry"]

- number: "832"
  prize: "no"
  informal_status:
    state: "disproved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "disproved"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory", "hypergraphs", "chromatic number"]

- number: "833"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory", "hypergraphs", "chromatic number"]

- number: "834"
  prize: "no"
  informal_status:
    state: "solved"
    last_update: "2026-01-01"
  formal_status:
    state: "unformalized"
  status:
    state: "solved"
    last_update: "2026-01-01"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory", "hypergraphs"]

- number: "835"
  prize: "no"
  informal_status:
    state: "verifiable"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "verifiable"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-01-26"
  tags: ["graph theory", "hypergraphs"]

- number: "836"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory", "hypergraphs", "chromatic number"]

- number: "837"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory", "hypergraphs"]

- number: "838"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["geometry", "convex"]

- number: "839"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "840"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["additive combinatorics", "sidon sets"]

- number: "841"
  prize: "no"
  informal_status:
    state: "solved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "solved"
    last_update: "2025-08-31"
  oeis: ["A092487"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "842"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory", "chromatic number"]

- number: "843"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "844"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2026-04-26"
  formal_status:
    state: "Lean"
    last_update: "2026-04-26"
  status:
    state: "proved (Lean)"
    last_update: "2026-04-26"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-08-04"
  tags: ["number theory", "intersecting family"]

- number: "845"
  prize: "no"
  informal_status:
    state: "disproved"
    last_update: "2026-01-08"
  formal_status:
    state: "Lean"
    last_update: "2026-01-08"
  status:
    state: "disproved (Lean)"
    last_update: "2026-01-08"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "846"
  prize: "no"
  informal_status:
    state: "disproved"
    last_update: "2026-02-25"
  formal_status:
    state: "Lean"
    last_update: "2026-02-25"
  status:
    state: "disproved (Lean)"
    last_update: "2026-02-25"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["geometry"]

- number: "847"
  prize: "no"
  informal_status:
    state: "disproved"
    last_update: "2026-01-19"
  formal_status:
    state: "unformalized"
  status:
    state: "disproved"
    last_update: "2026-01-19"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-01-22"
  tags: ["additive combinatorics"]

- number: "848"
  prize: "no"
  informal_status:
    state: "decidable"
    last_update: "2025-10-19"
  formal_status:
    state: "unformalized"
  status:
    state: "decidable"
    last_update: "2025-10-19"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-02-01"
  tags: ["number theory"]

- number: "849"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A003016", "A003015", "A059233", "A098565", "A090162", "A180058", "A182237"]
  formalized:
    state: "yes"
    last_update: "2025-12-17"
  comments: "Singmaster's conjecture"
  tags: ["number theory", "binomial coefficients"]

- number: "850"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A343101"]
  formalized:
    state: "yes"
    last_update: "2025-11-25"
  comments: "Erdős-Woods conjecture"
  tags: ["number theory", "primes"]

- number: "851"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2026-02-07"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2026-02-07"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-09-05"
  tags: ["number theory"]

- number: "852"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A001223", "A053597", "A078515"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory", "primes"]

- number: "853"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A001223", "A390769"]
  formalized:
    state: "yes"
    last_update: "2025-11-24"
  tags: ["number theory", "primes"]

- number: "854"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A389839", "A048670"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "855"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2026-03-14"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2026-03-14"
  oeis: ["A023193"]
  formalized:
    state: "yes"
    last_update: "2026-01-13"
  comments: "second Hardy-Littlewood conjecture"
  tags: ["number theory", "primes"]

- number: "856"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "857"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "yes"
    last_update: "2026-05-13"
  comments: "weak sunflower problem"
  tags: ["combinatorics"]

- number: "858"
  prize: "no"
  informal_status:
    state: "solved"
    last_update: "2026-04-24"
  formal_status:
    state: "unformalized"
  status:
    state: "solved"
    last_update: "2026-04-24"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory", "primitive sets"]

- number: "859"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-12-09"
  tags: ["number theory", "divisors"]

- number: "860"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A048670", "A058989"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory", "primes"]

- number: "861"
  prize: "no"
  informal_status:
    state: "solved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "solved"
    last_update: "2025-08-31"
  oeis: ["A143824", "A227590", "A003022", "A143823"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory", "sidon sets"]

- number: "862"
  prize: "no"
  informal_status:
    state: "solved"
    last_update: "2026-01-21"
  formal_status:
    state: "Lean"
    last_update: "2026-01-21"
  status:
    state: "solved (Lean)"
    last_update: "2026-01-21"
  oeis: ["A382395"]
  formalized:
    state: "yes"
    last_update: "2026-08-04"
  tags: ["number theory", "sidon sets"]

- number: "863"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2026-04-24"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2026-04-24"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory", "sidon sets", "additive combinatorics"]

- number: "864"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A389182"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory", "sidon sets", "additive combinatorics"]

- number: "865"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2026-07-02"
  formal_status:
    state: "Lean"
    last_update: "2026-07-02"
  status:
    state: "proved (Lean)"
    last_update: "2026-07-02"
  oeis: ["possible"]
  formalized:
    state: "yes"
    last_update: "2026-02-14"
  tags: ["number theory", "additive combinatorics"]

- number: "866"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory", "additive combinatorics"]

- number: "867"
  prize: "no"
  informal_status:
    state: "disproved"
    last_update: "2026-04-07"
  formal_status:
    state: "Lean"
    last_update: "2026-04-07"
  status:
    state: "disproved (Lean)"
    last_update: "2026-04-07"
  oeis: ["possible"]
  formalized:
    state: "yes"
    last_update: "2026-08-04"
  tags: ["additive combinatorics"]

- number: "868"
  prize: "no"
  informal_status:
    state: "solved"
    last_update: "2026-01-13"
  formal_status:
    state: "unformalized"
  status:
    state: "solved"
    last_update: "2026-01-13"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["number theory", "additive basis"]

- number: "869"
  prize: "no"
  informal_status:
    state: "disproved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "disproved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory", "additive basis"]

- number: "870"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory", "additive basis"]

- number: "871"
  prize: "no"
  informal_status:
    state: "disproved"
    last_update: "2026-01-05"
  formal_status:
    state: "Lean"
    last_update: "2026-01-05"
  status:
    state: "disproved (Lean)"
    last_update: "2026-01-05"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-06-26"
  tags: ["number theory", "additive basis"]

- number: "872"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "yes"
    last_update: "2026-07-02"
  tags: ["number theory", "primitive sets"]

- number: "873"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "874"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory", "additive combinatorics"]

- number: "875"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["additive combinatorics"]

- number: "876"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["additive combinatorics"]

- number: "877"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["A121269", "possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["additive combinatorics"]

- number: "878"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A339378", "possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "879"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A186736"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "880"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory", "additive basis"]

- number: "881"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-12-10"
  tags: ["number theory", "additive basis"]

- number: "882"
  prize: "no"
  informal_status:
    state: "solved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "solved"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory", "primitive sets"]

- number: "883"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory", "graph theory"]

- number: "884"
  prize: "no"
  informal_status:
    state: "disproved"
    last_update: "2026-07-03"
  formal_status:
    state: "Lean"
    last_update: "2026-07-03"
  status:
    state: "disproved (Lean)"
    last_update: "2026-07-03"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-05-07"
  tags: ["number theory", "divisors"]

- number: "885"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-01-05"
  tags: ["number theory", "divisors"]

- number: "886"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-02-01"
  tags: ["number theory", "divisors"]

- number: "887"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-01-13"
  tags: ["number theory", "divisors"]

- number: "888"
  prize: "no"
  informal_status:
    state: "solved"
    last_update: "2026-05-28"
  formal_status:
    state: "unformalized"
  status:
    state: "solved"
    last_update: "2026-05-28"
  oeis: ["A387584"]
  formalized:
    state: "yes"
    last_update: "2025-12-04"
  tags: ["number theory", "squares"]

- number: "889"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "yes"
    last_update: "2025-11-27"
  tags: ["number theory"]

- number: "890"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-02-02"
  tags: ["number theory", "primes"]

- number: "891"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-02-02"
  tags: ["number theory"]

- number: "892"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory", "primitive sets"]

- number: "893"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A046801", "possible"]
  formalized:
    state: "yes"
    last_update: "2025-09-25"
  tags: ["number theory", "divisors"]

- number: "894"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory", "ramsey theory"]

- number: "895"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["additive combinatorics", "graph theory"]

- number: "896"
  prize: "no"
  informal_status:
    state: "solved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "solved"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "897"
  prize: "no"
  informal_status:
    state: "disproved"
    last_update: "2025-12-27"
  formal_status:
    state: "Lean"
    last_update: "2025-12-27"
  status:
    state: "disproved (Lean)"
    last_update: "2025-12-27"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "898"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2026-02-02"
  formal_status:
    state: "Lean"
    last_update: "2026-02-02"
  status:
    state: "proved (Lean)"
    last_update: "2026-02-02"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-08-04"
  comments: "Erdős-Mordell inequality"
  tags: ["geometry"]

- number: "899"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["additive combinatorics"]

- number: "900"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory"]

- number: "901"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["combinatorics", "hypergraphs"]

- number: "902"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A362137"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory"]

- number: "903"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-10-14"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-10-14"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["combinatorics"]

- number: "904"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2026-04-18"
  formal_status:
    state: "Lean"
    last_update: "2026-04-18"
  status:
    state: "proved (Lean)"
    last_update: "2026-04-18"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-06-26"
  tags: ["graph theory"]

- number: "905"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2026-04-07"
  formal_status:
    state: "Lean"
    last_update: "2026-04-07"
  status:
    state: "proved (Lean)"
    last_update: "2026-04-07"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-08-04"
  tags: ["graph theory"]

- number: "906"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-01-02"
  tags: ["analysis", "iterated functions"]

- number: "907"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2026-04-07"
  formal_status:
    state: "Lean"
    last_update: "2026-04-07"
  status:
    state: "proved (Lean)"
    last_update: "2026-04-07"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-08-04"
  tags: ["analysis"]

- number: "908"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["analysis"]

- number: "909"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["analysis", "topology"]

- number: "910"
  prize: "no"
  informal_status:
    state: "disproved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "disproved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["topology"]

- number: "911"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory", "ramsey theory"]

- number: "912"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A071626"]
  formalized:
    state: "yes"
    last_update: "2026-01-26"
  tags: ["number theory", "factorials"]

- number: "913"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A359747"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "914"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2026-04-14"
  formal_status:
    state: "Lean"
    last_update: "2026-04-14"
  status:
    state: "proved (Lean)"
    last_update: "2026-04-14"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-08-04"
  tags: ["graph theory"]

- number: "915"
  prize: "no"
  informal_status:
    state: "solved"
    last_update: "2025-10-28"
  formal_status:
    state: "unformalized"
  status:
    state: "solved"
    last_update: "2025-10-28"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory"]

- number: "916"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory", "cycles"]

- number: "917"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory", "chromatic number"]

- number: "918"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-11-21"
  tags: ["graph theory", "chromatic number"]

- number: "919"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory", "chromatic number"]

- number: "920"
  prize: "no"
  informal_status:
    state: "solved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "solved"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "yes"
    last_update: "2026-02-05"
  tags: ["graph theory", "chromatic number"]

- number: "921"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory", "chromatic number", "cycles"]

- number: "922"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory", "chromatic number"]

- number: "923"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2026-04-20"
  formal_status:
    state: "Lean"
    last_update: "2026-04-20"
  status:
    state: "proved (Lean)"
    last_update: "2026-04-20"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-06-26"
  tags: ["graph theory", "chromatic number"]

- number: "924"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory", "ramsey theory"]

- number: "925"
  prize: "no"
  informal_status:
    state: "disproved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "disproved"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory", "ramsey theory"]

- number: "926"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory"]

- number: "927"
  prize: "no"
  informal_status:
    state: "disproved"
    last_update: "2026-06-07"
  formal_status:
    state: "Lean"
    last_update: "2026-06-07"
  status:
    state: "disproved (Lean)"
    last_update: "2026-06-07"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory"]

- number: "928"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-09-04"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-09-04"
  oeis: ["A006530"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "929"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "930"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-12-10"
  tags: ["number theory"]

- number: "931"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "932"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A387864"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "933"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "yes"
    last_update: "2026-07-02"
  tags: ["number theory"]

- number: "934"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory"]

- number: "935"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-09-04"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-09-04"
  oeis: ["A057521", "A389244", "possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "936"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A146968", "possible"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "937"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "yes"
    last_update: "2026-06-24"
  tags: ["number theory"]

- number: "938"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A001694", "A076446", "possible"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "939"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "yes"
    last_update: "2025-09-01"
  tags: ["number theory"]

- number: "940"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "941"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["A056828"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "942"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "943"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "944"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-09-02"
  tags: ["graph theory", "chromatic number"]

- number: "945"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["possible", "A048892"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["number theory", "divisors"]

- number: "946"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["A005237", "A284783"]
  formalized:
    state: "yes"
    last_update: "2025-09-18"
  tags: ["number theory", "divisors"]

- number: "947"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2026-02-02"
  formal_status:
    state: "Lean"
    last_update: "2026-02-02"
  status:
    state: "proved (Lean)"
    last_update: "2026-02-02"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory", "covering systems"]

- number: "948"
  prize: "no"
  informal_status:
    state: "solved"
    last_update: "2026-07-06"
  formal_status:
    state: "unformalized"
  status:
    state: "solved"
    last_update: "2026-07-06"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory", "ramsey theory"]

- number: "949"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-08-31"
  tags: ["ramsey theory"]

- number: "950"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-06-17"
  tags: ["number theory", "primes"]

- number: "951"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-01-28"
  tags: ["number theory"]

- number: "952"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-11-21"
  comments: "Gaussian moat problem"
  tags: ["number theory"]

- number: "953"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["geometry", "distances"]

- number: "954"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A390642"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "955"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "yes"
    last_update: "2026-08-05"
  tags: ["number theory"]

- number: "956"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["geometry", "distances", "convex"]

- number: "957"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-09-07"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-09-07"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["geometry", "distances"]

- number: "958"
  prize: "no"
  informal_status:
    state: "disproved"
    last_update: "2025-12-27"
  formal_status:
    state: "Lean"
    last_update: "2025-12-27"
  status:
    state: "disproved (Lean)"
    last_update: "2025-12-27"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-08-04"
  tags: ["distances", "geometry"]

- number: "959"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-08-07"
  tags: ["geometry", "distances"]

- number: "960"
  prize: "no"
  informal_status:
    state: "disproved"
    last_update: "2026-04-09"
  formal_status:
    state: "unformalized"
  status:
    state: "disproved"
    last_update: "2026-04-09"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["geometry"]

- number: "961"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A213253"]
  formalized:
    state: "yes"
    last_update: "2025-12-30"
  tags: ["number theory"]

- number: "962"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A327909"]
  formalized:
    state: "yes"
    last_update: "2026-05-03"
  tags: ["number theory"]

- number: "963"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "964"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2026-02-14"
  formal_status:
    state: "Lean"
    last_update: "2026-02-14"
  status:
    state: "proved (Lean)"
    last_update: "2026-02-14"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory", "divisors"]

- number: "965"
  prize: "no"
  informal_status:
    state: "disproved"
    last_update: "2026-01-01"
  formal_status:
    state: "unformalized"
  status:
    state: "disproved"
    last_update: "2026-01-01"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-01-22"
  tags: ["ramsey theory"]

- number: "966"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2026-02-25"
  formal_status:
    state: "Lean"
    last_update: "2026-02-25"
  status:
    state: "proved (Lean)"
    last_update: "2026-02-25"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-08-04"
  tags: ["number theory", "additive combinatorics", "ramsey theory"]

- number: "967"
  prize: "no"
  informal_status:
    state: "disproved"
    last_update: "2025-12-19"
  formal_status:
    state: "Lean"
    last_update: "2025-12-19"
  status:
    state: "disproved (Lean)"
    last_update: "2025-12-19"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-08-04"
  tags: ["number theory", "analysis"]

- number: "968"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A387591"]
  formalized:
    state: "yes"
    last_update: "2026-01-12"
  tags: ["number theory"]

- number: "969"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A013928"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "970"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A048669"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  comments: "Jacobsthal's function"
  tags: ["number theory"]

- number: "971"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A226521"]
  formalized:
    state: "yes"
    last_update: "2026-01-12"
  tags: ["number theory"]

- number: "972"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2025-12-07"
  tags: ["number theory"]

- number: "973"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-06-07"
  tags: ["analysis"]

- number: "974"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2026-04-27"
  formal_status:
    state: "Lean"
    last_update: "2026-04-27"
  status:
    state: "proved (Lean)"
    last_update: "2026-04-27"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-08-04"
  tags: ["analysis"]

- number: "975"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A147807", "possible"]
  formalized:
    state: "yes"
    last_update: "2025-12-20"
  tags: ["number theory", "divisors"]

- number: "976"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "977"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["A005420", "A002583"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "978"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "yes"
    last_update: "2026-01-20"
  tags: ["number theory"]

- number: "979"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A385316", "possible"]
  formalized:
    state: "yes"
    last_update: "2025-10-16"
  tags: ["number theory"]

- number: "980"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-09-03"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-09-03"
  oeis: ["A053760", "A098990", "possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "981"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-12-26"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-12-26"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "982"
  prize: "no"
  informal_status:
    state: "falsifiable"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "falsifiable"
    last_update: "2025-08-31"
  oeis: ["A004526"]
  formalized:
    state: "yes"
    last_update: "2025-11-13"
  tags: ["geometry", "convex", "distances"]

- number: "983"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["number theory"]

- number: "984"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-08-31"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["arithmetic progressions", "additive combinatorics"]

- number: "985"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-08-31"
  oeis: ["A002233", "A219429", "A103309", "possible"]
  formalized:
    state: "yes"
    last_update: "2025-09-07"
  tags: ["number theory"]

- number: "986"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2026-06-21"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2026-06-21"
  oeis: ["A000791", "A059442"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["graph theory", "ramsey theory"]

- number: "987"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2026-04-09"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2026-04-09"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-07-02"
  tags: ["analysis", "discrepancy"]

- number: "988"
  prize: "no"
  informal_status:
    state: "solved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "solved"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["discrepancy"]

- number: "989"
  prize: "no"
  informal_status:
    state: "solved"
    last_update: "2025-08-31"
  formal_status:
    state: "unformalized"
  status:
    state: "solved"
    last_update: "2025-08-31"
  oeis: ["possible"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["discrepancy"]

- number: "990"
  prize: "no"
  informal_status:
    state: "disproved"
    last_update: "2026-04-19"
  formal_status:
    state: "Lean"
    last_update: "2026-04-19"
  status:
    state: "disproved (Lean)"
    last_update: "2026-04-19"
  oeis: ["N/A"]
  formalized:
    state: "yes"
    last_update: "2026-08-04"
  tags: ["analysis"]

- number: "991"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-09-16"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-09-16"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["discrepancy"]

- number: "992"
  prize: "no"
  informal_status:
    state: "disproved"
    last_update: "2026-02-01"
  formal_status:
    state: "unformalized"
  status:
    state: "disproved"
    last_update: "2026-02-01"
  oeis: ["N/A"]
  formalized:
    state: "no"
    last_update: "2025-08-31"
  tags: ["discrepancy"]

- number: "993"
  prize: "no"
  informal_status:
    state: "falsifiable"
    last_update: "2025-09-07"
  formal_status:
    state: "unformalized"
  status:
    state: "falsifiable"
    last_update: "2025-09-07"
  formalized:
    state: "no"
    last_update: "2025-09-07"
  oeis: ["A000055", "possible"]
  tags: ["graph theory"]

- number: "994"
  prize: "no"
  informal_status:
    state: "disproved"
    last_update: "2025-09-07"
  formal_status:
    state: "unformalized"
  status:
    state: "disproved"
    last_update: "2025-09-07"
  formalized:
    state: "no"
    last_update: "2025-09-07"
  oeis: ["N/A"]
  tags: ["analysis", "discrepancy"]

- number: "995"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-09-07"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-09-07"
  formalized:
    state: "no"
    last_update: "2025-09-07"
  oeis: ["N/A"]
  tags: ["analysis", "discrepancy"]

- number: "996"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-09-07"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-09-07"
  formalized:
    state: "yes"
    last_update: "2025-12-22"
  oeis: ["N/A"]
  tags: ["analysis"]

- number: "997"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2026-04-03"
  formal_status:
    state: "Lean"
    last_update: "2026-04-03"
  status:
    state: "proved (Lean)"
    last_update: "2026-04-03"
  formalized:
    state: "yes"
    last_update: "2026-02-14"
  oeis: ["N/A"]
  tags: ["analysis", "discrepancy", "primes"]

- number: "998"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-09-07"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-09-07"
  formalized:
    state: "no"
    last_update: "2025-09-07"
  oeis: ["N/A"]
  tags: ["analysis", "diophantine approximation"]

- number: "999"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-09-07"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-09-07"
  formalized:
    state: "no"
    last_update: "2025-09-07"
  oeis: ["N/A"]
  comments: "Duffin-Schaeffer conjecture"
  tags: ["number theory", "diophantine approximation"]

- number: "1000"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-12-27"
  formal_status:
    state: "Lean"
    last_update: "2025-12-27"
  status:
    state: "proved (Lean)"
    last_update: "2025-12-27"
  formalized:
    state: "yes"
    last_update: "2026-08-04"
  oeis: ["N/A"]
  tags: ["number theory", "diophantine approximation"]

- number: "1001"
  prize: "no"
  informal_status:
    state: "solved"
    last_update: "2025-09-07"
  formal_status:
    state: "unformalized"
  status:
    state: "solved"
    last_update: "2025-09-07"
  formalized:
    state: "no"
    last_update: "2025-09-07"
  oeis: ["N/A"]
  tags: ["number theory", "diophantine approximation"]

- number: "1002"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-09-07"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-09-07"
  formalized:
    state: "yes"
    last_update: "2026-04-28"
  oeis: ["N/A"]
  tags: ["analysis", "diophantine approximation"]

- number: "1003"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-09-08"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-09-08"
  formalized:
    state: "yes"
    last_update: "2025-10-06"
  oeis: ["A001274"]
  tags: ["number theory"]

- number: "1004"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-09-07"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-09-07"
  formalized:
    state: "yes"
    last_update: "2025-12-10"
  oeis: ["possible"]
  tags: ["number theory"]

- number: "1005"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-09-09"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-09-09"
  formalized:
    state: "no"
    last_update: "2025-09-09"
  oeis: ["A386893"]
  tags: ["number theory"]

- number: "1006"
  prize: "no"
  informal_status:
    state: "disproved"
    last_update: "2025-09-28"
  formal_status:
    state: "unformalized"
  status:
    state: "disproved"
    last_update: "2025-09-28"
  formalized:
    state: "no"
    last_update: "2025-09-09"
  oeis: ["N/A"]
  tags: ["graph theory", "cycles"]

- number: "1007"
  prize: "no"
  informal_status:
    state: "solved"
    last_update: "2026-01-19"
  formal_status:
    state: "Lean"
    last_update: "2026-01-19"
  status:
    state: "solved (Lean)"
    last_update: "2026-01-19"
  formalized:
    state: "yes"
    last_update: "2026-08-05"
  oeis: ["N/A"]
  tags: ["graph theory"]

- number: "1008"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2026-01-17"
  formal_status:
    state: "Lean"
    last_update: "2026-01-17"
  status:
    state: "proved (Lean)"
    last_update: "2026-01-17"
  formalized:
    state: "yes"
    last_update: "2026-08-05"
  oeis: ["N/A"]
  tags: ["graph theory"]

- number: "1009"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-10-31"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-10-31"
  formalized:
    state: "no"
    last_update: "2025-09-10"
  oeis: ["N/A"]
  tags: ["graph theory"]

- number: "1010"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-09-10"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-09-10"
  formalized:
    state: "no"
    last_update: "2025-09-10"
  oeis: ["N/A"]
  tags: ["graph theory"]

- number: "1011"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-09-10"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-09-10"
  formalized:
    state: "no"
    last_update: "2025-09-10"
  oeis: ["possible"]
  tags: ["graph theory"]

- number: "1012"
  prize: "no"
  informal_status:
    state: "solved"
    last_update: "2025-10-31"
  formal_status:
    state: "unformalized"
  status:
    state: "solved"
    last_update: "2025-10-31"
  formalized:
    state: "no"
    last_update: "2025-09-10"
  tags: ["graph theory"]

- number: "1013"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-09-10"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-09-10"
  formalized:
    state: "no"
    last_update: "2025-09-10"
  oeis: ["A292528"]
  tags: ["graph theory"]

- number: "1014"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2026-04-24"
  formal_status:
    state: "Lean"
    last_update: "2026-04-24"
  status:
    state: "proved (Lean)"
    last_update: "2026-04-24"
  formalized:
    state: "yes"
    last_update: "2026-08-05"
  oeis: ["possible"]
  tags: ["graph theory"]

- number: "1015"
  prize: "no"
  informal_status:
    state: "solved"
    last_update: "2025-09-10"
  formal_status:
    state: "unformalized"
  status:
    state: "solved"
    last_update: "2025-09-10"
  formalized:
    state: "no"
    last_update: "2025-09-10"
  oeis: ["possible"]
  tags: ["graph theory", "ramsey theory"]

- number: "1016"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-09-10"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-09-10"
  formalized:
    state: "no"
    last_update: "2025-09-10"
  oeis: ["A105206"]
  comments: "pancyclic graphs"
  tags: ["graph theory", "cycles"]
- number: "1017"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-09-12"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-09-12"
  formalized:
    state: "no"
    last_update: "2025-09-10"
  oeis: ["possible"]
  tags: ["graph theory"]

- number: "1018"
  prize: "no"
  informal_status:
    state: "solved"
    last_update: "2025-12-12"
  formal_status:
    state: "unformalized"
  status:
    state: "solved"
    last_update: "2025-12-12"
  formalized:
    state: "no"
    last_update: "2025-09-10"
  oeis: ["N/A"]
  tags: ["graph theory", "planar graphs"]

- number: "1019"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-11-21"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-11-21"
  formalized:
    state: "no"
    last_update: "2025-09-10"
  oeis: ["N/A"]
  tags: ["graph theory", "planar graphs"]

- number: "1020"
  prize: "no"
  informal_status:
    state: "falsifiable"
    last_update: "2025-09-12"
  formal_status:
    state: "unformalized"
  status:
    state: "falsifiable"
    last_update: "2025-09-12"
  formalized:
    state: "no"
    last_update: "2025-09-10"
  oeis: ["N/A"]
  comments: "Erdős matching conjecture"
  tags: ["graph theory", "hypergraphs"]

- number: "1021"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2026-01-20"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2026-01-20"
  formalized:
    state: "no"
    last_update: "2025-09-10"
  oeis: ["N/A"]
  tags: ["graph theory"]

- number: "1022"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2026-01-23"
  formal_status:
    state: "Lean"
    last_update: "2026-01-23"
  status:
    state: "proved (Lean)"
    last_update: "2026-01-23"
  formalized:
    state: "yes"
    last_update: "2026-08-05"
  oeis: ["possible"]
  tags: ["combinatorics", "hypergraphs"]

- number: "1023"
  prize: "no"
  informal_status:
    state: "solved"
    last_update: "2026-02-10"
  formal_status:
    state: "Lean"
    last_update: "2026-02-10"
  status:
    state: "solved (Lean)"
    last_update: "2026-02-10"
  formalized:
    state: "yes"
    last_update: "2026-08-05"
  oeis: ["A347025", "possible"]
  tags: ["combinatorics"]

- number: "1024"
  prize: "no"
  informal_status:
    state: "solved"
    last_update: "2025-09-12"
  formal_status:
    state: "unformalized"
  status:
    state: "solved"
    last_update: "2025-09-12"
  formalized:
    state: "no"
    last_update: "2025-09-10"
  oeis: ["possible"]
  tags: ["graph theory", "hypergraphs"]

- number: "1025"
  prize: "no"
  informal_status:
    state: "solved"
    last_update: "2025-09-12"
  formal_status:
    state: "unformalized"
  status:
    state: "solved"
    last_update: "2025-09-12"
  formalized:
    state: "no"
    last_update: "2025-09-10"
  oeis: ["possible"]
  tags: ["combinatorics"]

- number: "1026"
  prize: "no"
  informal_status:
    state: "solved"
    last_update: "2025-12-12"
  formal_status:
    state: "Lean"
    last_update: "2025-12-12"
  status:
    state: "solved (Lean)"
    last_update: "2025-12-12"
  formalized:
    state: "yes"
    last_update: "2026-08-05"
  oeis: ["A391431", "A391490"]
  tags: ["combinatorics"]

- number: "1027"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-10-01"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-10-01"
  formalized:
    state: "no"
    last_update: "2025-09-10"
  oeis: ["N/A"]
  tags: ["combinatorics"]

- number: "1028"
  prize: "no"
  informal_status:
    state: "solved"
    last_update: "2026-01-19"
  formal_status:
    state: "Lean"
    last_update: "2026-01-19"
  status:
    state: "solved (Lean)"
    last_update: "2026-01-19"
  formalized:
    state: "yes"
    last_update: "2026-08-05"
  oeis: ["possible"]
  tags: ["graph theory", "discrepancy"]

- number: "1029"
  prize: "$100"
  informal_status:
    state: "open"
    last_update: "2025-09-13"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-09-13"
  formalized:
    state: "no"
    last_update: "2025-09-10"
  oeis: ["A059442"]
  tags: ["graph theory", "ramsey theory"]

- number: "1030"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-09-13"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-09-13"
  formalized:
    state: "no"
    last_update: "2025-09-10"
  oeis: ["A000791", "A059442"]
  tags: ["graph theory", "ramsey theory"]

- number: "1031"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-09-13"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-09-13"
  formalized:
    state: "no"
    last_update: "2025-09-10"
  oeis: ["possible"]
  tags: ["graph theory"]

- number: "1032"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-09-13"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-09-13"
  formalized:
    state: "no"
    last_update: "2025-09-10"
  oeis: ["possible"]
  tags: ["graph theory", "chromatic number"]

- number: "1033"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-12-12"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-12-12"
  formalized:
    state: "no"
    last_update: "2025-09-10"
  oeis: ["possible"]
  tags: ["graph theory"]

- number: "1034"
  prize: "no"
  informal_status:
    state: "disproved"
    last_update: "2025-12-04"
  formal_status:
    state: "Lean"
    last_update: "2025-12-04"
  status:
    state: "disproved (Lean)"
    last_update: "2025-12-04"
  formalized:
    state: "yes"
    last_update: "2026-08-05"
  oeis: ["possible"]
  tags: ["graph theory"]

- number: "1035"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-12-26"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-12-26"
  formalized:
    state: "no"
    last_update: "2025-09-10"
  oeis: ["possible"]
  tags: ["graph theory"]

- number: "1036"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2026-01-20"
  formal_status:
    state: "Lean"
    last_update: "2026-01-20"
  status:
    state: "proved (Lean)"
    last_update: "2026-01-20"
  formalized:
    state: "yes"
    last_update: "2026-08-05"
  oeis: ["possible"]
  tags: ["graph theory"]

- number: "1037"
  prize: "no"
  informal_status:
    state: "disproved"
    last_update: "2026-01-18"
  formal_status:
    state: "Lean"
    last_update: "2026-01-18"
  status:
    state: "disproved (Lean)"
    last_update: "2026-01-18"
  formalized:
    state: "yes"
    last_update: "2026-08-05"
  oeis: ["N/A"]
  tags: ["graph theory"]

- number: "1038"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-09-15"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-09-15"
  formalized:
    state: "yes"
    last_update: "2025-12-31"
  oeis: ["N/A"]
  tags: ["analysis"]

- number: "1039"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-09-15"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-09-15"
  formalized:
    state: "no"
    last_update: "2025-09-10"
  oeis: ["N/A"]
  tags: ["analysis"]

- number: "1040"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-09-15"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-09-15"
  formalized:
    state: "no"
    last_update: "2025-09-10"
  oeis: ["N/A"]
  tags: ["analysis"]

- number: "1041"
  prize: "no"
  informal_status:
    state: "falsifiable"
    last_update: "2025-09-15"
  formal_status:
    state: "unformalized"
  status:
    state: "falsifiable"
    last_update: "2025-09-15"
  formalized:
    state: "yes"
    last_update: "2025-11-26"
  oeis: ["N/A"]
  tags: ["analysis"]

- number: "1042"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-09-15"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-09-15"
  formalized:
    state: "no"
    last_update: "2025-09-10"
  oeis: ["N/A"]
  tags: ["analysis"]

- number: "1043"
  prize: "no"
  informal_status:
    state: "disproved"
    last_update: "2025-12-28"
  formal_status:
    state: "Lean"
    last_update: "2025-12-28"
  status:
    state: "disproved (Lean)"
    last_update: "2025-12-28"
  formalized:
    state: "yes"
    last_update: "2025-12-20"
  oeis: ["N/A"]
  tags: ["analysis"]

- number: "1044"
  prize: "no"
  informal_status:
    state: "solved"
    last_update: "2026-04-28"
  formal_status:
    state: "Lean"
    last_update: "2026-04-28"
  status:
    state: "solved (Lean)"
    last_update: "2026-04-28"
  formalized:
    state: "yes"
    last_update: "2026-08-04"
  oeis: ["N/A"]
  tags: ["analysis"]

- number: "1045"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2026-03-14"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2026-03-14"
  formalized:
    state: "no"
    last_update: "2025-09-10"
  oeis: ["N/A"]
  tags: ["analysis"]

- number: "1046"
  prize: "no"
  informal_status:
    state: "disproved"
    last_update: "2025-09-15"
  formal_status:
    state: "unformalized"
  status:
    state: "disproved"
    last_update: "2025-09-15"
  formalized:
    state: "no"
    last_update: "2025-09-10"
  oeis: ["N/A"]
  tags: ["analysis"]

- number: "1047"
  prize: "no"
  informal_status:
    state: "disproved"
    last_update: "2026-01-21"
  formal_status:
    state: "Lean"
    last_update: "2026-01-21"
  status:
    state: "disproved (Lean)"
    last_update: "2026-01-21"
  formalized:
    state: "yes"
    last_update: "2026-08-04"
  oeis: ["N/A"]
  tags: ["analysis"]

- number: "1048"
  prize: "no"
  informal_status:
    state: "disproved"
    last_update: "2026-01-27"
  formal_status:
    state: "Lean"
    last_update: "2026-01-27"
  status:
    state: "disproved (Lean)"
    last_update: "2026-01-27"
  formalized:
    state: "yes"
    last_update: "2026-08-04"
  oeis: ["N/A"]
  tags: ["analysis"]

- number: "1049"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-09-28"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-09-28"
  formalized:
    state: "yes"
    last_update: "2026-02-15"
  oeis: ["N/A"]
  tags: ["irrationality"]

- number: "1050"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-09-28"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-09-28"
  formalized:
    state: "no"
    last_update: "2025-09-28"
  oeis: ["A331372"]
  tags: ["irrationality"]

- number: "1051"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2026-01-29"
  formal_status:
    state: "Lean"
    last_update: "2026-01-29"
  status:
    state: "proved (Lean)"
    last_update: "2026-01-29"
  formalized:
    state: "yes"
    last_update: "2025-11-24"
  oeis: ["N/A"]
  tags: ["irrationality"]

- number: "1052"
  prize: "$10"
  informal_status:
    state: "open"
    last_update: "2025-09-28"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-09-28"
  formalized:
    state: "yes"
    last_update: "2025-10-10"
  oeis: ["A002827"]
  comments: "unitary perfect numbers"
  tags: ["number theory"]

- number: "1053"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-09-28"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-09-28"
  formalized:
    state: "no"
    last_update: "2025-09-28"
  oeis: ["A007539"]
  comments: "multiply perfect numbers"
  tags: ["number theory"]

- number: "1054"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-09-28"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-09-28"
  formalized:
    state: "yes"
    last_update: "2025-11-25"
  oeis: ["A167485"]
  tags: ["number theory", "divisors"]

- number: "1055"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-09-28"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-09-28"
  formalized:
    state: "yes"
    last_update: "2025-11-13"
  oeis: ["A005113"]
  tags: ["number theory", "primes"]

- number: "1056"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-09-28"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-09-28"
  formalized:
    state: "yes"
    last_update: "2025-10-24"
  oeis: ["A060427"]
  tags: ["number theory"]

- number: "1057"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-09-28"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-09-28"
  formalized:
    state: "yes"
    last_update: "2026-06-15"
  oeis: ["A006931"]
  comments: "Carmichael numbers"
  tags: ["number theory"]

- number: "1058"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-09-28"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-09-28"
  formalized:
    state: "no"
    last_update: "2025-09-28"
  oeis: ["N/A"]
  tags: ["number theory"]

- number: "1059"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-09-28"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-09-28"
  formalized:
    state: "yes"
    last_update: "2025-11-02"
  oeis: ["A064152"]
  tags: ["number theory", "primes"]

- number: "1060"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-09-28"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-09-28"
  formalized:
    state: "yes"
    last_update: "2025-12-13"
  oeis: ["A327153"]
  tags: ["number theory"]

- number: "1061"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-09-28"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-09-28"
  formalized:
    state: "yes"
    last_update: "2026-01-12"
  oeis: ["A110177", "possible"]
  tags: ["number theory"]

- number: "1062"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-09-28"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-09-28"
  formalized:
    state: "yes"
    last_update: "2026-01-05"
  oeis: ["A038372"]
  tags: ["number theory"]

- number: "1063"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-10-01"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-10-01"
  formalized:
    state: "yes"
    last_update: "2026-01-23"
  oeis: ["A389360"]
  tags: ["number theory"]

- number: "1064"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-12-12"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-12-12"
  formalized:
    state: "yes"
    last_update: "2025-12-10"
  oeis: ["A051488", "A051487"]
  tags: ["number theory"]

- number: "1065"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-10-01"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-10-01"
  formalized:
    state: "yes"
    last_update: "2025-10-15"
  oeis: ["A074781", "A339465"]
  tags: ["number theory"]

- number: "1066"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-10-01"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-10-01"
  formalized:
    state: "no"
    last_update: "2025-09-28"
  oeis: ["possible"]
  tags: ["graph theory", "planar graphs"]

- number: "1067"
  prize: "no"
  informal_status:
    state: "disproved"
    last_update: "2026-02-02"
  formal_status:
    state: "Lean"
    last_update: "2026-02-02"
  status:
    state: "disproved (Lean)"
    last_update: "2026-02-02"
  formalized:
    state: "yes"
    last_update: "2026-01-14"
  oeis: ["N/A"]
  tags: ["graph theory", "set theory"]

- number: "1068"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-10-01"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-10-01"
  formalized:
    state: "yes"
    last_update: "2026-01-09"
  oeis: ["N/A"]
  tags: ["graph theory", "set theory", "chromatic number"]

- number: "1069"
  prize: "no"
  informal_status:
    state: "solved"
    last_update: "2025-10-05"
  formal_status:
    state: "unformalized"
  status:
    state: "solved"
    last_update: "2025-10-05"
  formalized:
    state: "no"
    last_update: "2025-09-28"
  oeis: ["possible"]
  tags: ["geometry"]

- number: "1070"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-10-05"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-10-05"
  formalized:
    state: "no"
    last_update: "2025-09-28"
  oeis: ["possible"]
  tags: ["geometry"]

- number: "1071"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2026-02-12"
  formal_status:
    state: "Lean"
    last_update: "2026-02-12"
  status:
    state: "proved (Lean)"
    last_update: "2026-02-12"
  formalized:
    state: "yes"
    last_update: "2026-01-11"
  oeis: ["N/A"]
  tags: ["geometry"]

- number: "1072"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-10-05"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-10-05"
  formalized:
    state: "yes"
    last_update: "2025-12-17"
  oeis: ["A073944", "A072937", "A154554"]
  tags: ["number theory"]

- number: "1073"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-10-05"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-10-05"
  formalized:
    state: "yes"
    last_update: "2025-11-13"
  oeis: ["A256519"]
  tags: ["number theory"]

- number: "1074"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-10-05"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-10-05"
  formalized:
    state: "yes"
    last_update: "2025-11-21"
  oeis: ["A063980", "A064164"]
  tags: ["number theory"]

- number: "1075"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-10-05"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-10-05"
  formalized:
    state: "no"
    last_update: "2025-09-28"
  oeis: ["N/A"]
  tags: ["hypergraphs"]

- number: "1076"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-12-12"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-12-12"
  formalized:
    state: "no"
    last_update: "2025-09-28"
  oeis: ["possible"]
  tags: ["hypergraphs"]

- number: "1077"
  prize: "no"
  informal_status:
    state: "disproved"
    last_update: "2025-12-29"
  formal_status:
    state: "unformalized"
  status:
    state: "disproved"
    last_update: "2025-12-29"
  formalized:
    state: "yes"
    last_update: "2025-10-17"
  oeis: ["N/A"]
  tags: ["graph theory"]

- number: "1078"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-10-06"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-10-06"
  formalized:
    state: "no"
    last_update: "2025-09-28"
  oeis: ["N/A"]
  tags: ["graph theory"]

- number: "1079"
  prize: "no"
  informal_status:
    state: "solved"
    last_update: "2025-10-14"
  formal_status:
    state: "unformalized"
  status:
    state: "solved"
    last_update: "2025-10-14"
  formalized:
    state: "no"
    last_update: "2025-09-28"
  oeis: ["N/A"]
  tags: ["graph theory", "turan number"]

- number: "1080"
  prize: "no"
  informal_status:
    state: "disproved"
    last_update: "2025-12-28"
  formal_status:
    state: "Lean"
    last_update: "2025-12-28"
  status:
    state: "disproved (Lean)"
    last_update: "2025-12-28"
  formalized:
    state: "yes"
    last_update: "2025-12-11"
  oeis: ["possible"]
  tags: ["graph theory"]

- number: "1081"
  prize: "no"
  informal_status:
    state: "disproved"
    last_update: "2025-10-14"
  formal_status:
    state: "unformalized"
  status:
    state: "disproved"
    last_update: "2025-10-14"
  formalized:
    state: "no"
    last_update: "2025-09-28"
  oeis: ["A076871", "A076872", "possible"]
  tags: ["number theory", "powerful"]

- number: "1082"
  prize: "no"
  informal_status:
    state: "falsifiable"
    last_update: "2025-10-17"
  formal_status:
    state: "unformalized"
  status:
    state: "falsifiable"
    last_update: "2025-10-17"
  formalized:
    state: "yes"
    last_update: "2026-02-25"
  oeis: ["possible"]
  tags: ["geometry", "distances"]

- number: "1083"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-10-17"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-10-17"
  formalized:
    state: "no"
    last_update: "2025-09-28"
  oeis: ["A186704", "possible"]
  tags: ["geometry", "distances"]

- number: "1084"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-10-17"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-10-17"
  formalized:
    state: "yes"
    last_update: "2025-12-30"
  comments: "contact number problem"
  oeis: ["A045945", "possible"]
  tags: ["geometry", "distances"]

- number: "1085"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-10-17"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-10-17"
  formalized:
    state: "yes"
    last_update: "2025-12-31"
  oeis: ["A186705", "possible"]
  tags: ["geometry", "distances"]

- number: "1086"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-10-17"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-10-17"
  formalized:
    state: "no"
    last_update: "2025-09-28"
  oeis: ["possible"]
  tags: ["geometry", "distances"]

- number: "1087"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-10-17"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-10-17"
  formalized:
    state: "no"
    last_update: "2025-09-28"
  oeis: ["possible"]
  tags: ["geometry", "distances"]

- number: "1088"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-10-17"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-10-17"
  formalized:
    state: "no"
    last_update: "2025-09-28"
  oeis: ["possible"]
  tags: ["geometry"]

- number: "1089"
  prize: "no"
  informal_status:
    state: "solved"
    last_update: "2026-02-01"
  formal_status:
    state: "unformalized"
  status:
    state: "solved"
    last_update: "2026-02-01"
  formalized:
    state: "no"
    last_update: "2025-09-28"
  oeis: ["possible"]
  tags: ["geometry", "distances"]

- number: "1090"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2026-02-27"
  formal_status:
    state: "Lean"
    last_update: "2026-02-27"
  status:
    state: "proved (Lean)"
    last_update: "2026-02-27"
  formalized:
    state: "yes"
    last_update: "2026-06-26"
  oeis: ["N/A"]
  tags: ["geometry", "ramsey theory"]

- number: "1091"
  prize: "no"
  informal_status:
    state: "solved"
    last_update: "2026-04-09"
  formal_status:
    state: "unformalized"
  status:
    state: "solved"
    last_update: "2026-04-09"
  formalized:
    state: "no"
    last_update: "2025-09-28"
  oeis: ["N/A"]
  tags: ["geometry", "chromatic number"]

- number: "1092"
  prize: "no"
  informal_status:
    state: "disproved"
    last_update: "2025-10-17"
  formal_status:
    state: "unformalized"
  status:
    state: "disproved"
    last_update: "2025-10-17"
  formalized:
    state: "yes"
    last_update: "2026-01-08"
  oeis: ["N/A"]
  tags: ["geometry", "chromatic number"]

- number: "1093"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-10-18"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-10-18"
  formalized:
    state: "yes"
    last_update: "2025-12-12"
  oeis: ["N/A"]
  tags: ["number theory", "binomial coefficients"]

- number: "1094"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-10-18"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-10-18"
  formalized:
    state: "yes"
    last_update: "2025-12-10"
  oeis: ["N/A"]
  tags: ["number theory", "binomial coefficients"]

- number: "1095"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-10-18"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-10-18"
  formalized:
    state: "yes"
    last_update: "2025-12-29"
  oeis: ["A003458"]
  tags: ["number theory", "binomial coefficients"]

- number: "1096"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2026-04-24"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2026-04-24"
  formalized:
    state: "yes"
    last_update: "2026-05-21"
  oeis: ["N/A"]
  tags: ["number theory"]

- number: "1097"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-10-18"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-10-18"
  formalized:
    state: "yes"
    last_update: "2025-12-11"
  oeis: ["N/A"]
  tags: ["number theory", "additive combinatorics"]

- number: "1098"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2026-05-02"
  formal_status:
    state: "Lean"
    last_update: "2026-05-02"
  status:
    state: "proved (Lean)"
    last_update: "2026-05-02"
  formalized:
    state: "yes"
    last_update: "2026-08-04"
  oeis: ["N/A"]
  tags: ["group theory"]

- number: "1099"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-10-19"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-10-19"
  formalized:
    state: "no"
    last_update: "2025-09-28"
  oeis: ["N/A"]
  tags: ["number theory", "divisors"]

- number: "1100"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-10-19"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-10-19"
  formalized:
    state: "no"
    last_update: "2025-09-28"
  oeis: ["A325864", "possible"]
  tags: ["number theory", "divisors"]

- number: "1101"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-10-19"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-10-19"
  formalized:
    state: "yes"
    last_update: "2025-12-26"
  oeis: ["N/A"]
  tags: ["number theory"]

- number: "1102"
  prize: "no"
  informal_status:
    state: "solved"
    last_update: "2026-02-23"
  formal_status:
    state: "Lean"
    last_update: "2026-02-23"
  status:
    state: "solved (Lean)"
    last_update: "2026-02-23"
  formalized:
    state: "yes"
    last_update: "2025-12-24"
  oeis: ["N/A"]
  tags: ["number theory"]

- number: "1103"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-10-19"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-10-19"
  formalized:
    state: "no"
    last_update: "2025-09-28"
  oeis: ["A392164"]
  tags: ["number theory"]

- number: "1104"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-10-26"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-10-26"
  formalized:
    state: "yes"
    last_update: "2025-12-11"
  oeis: ["A292528"]
  tags: ["graph theory", "chromatic number"]

- number: "1105"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2026-02-01"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2026-02-01"
  formalized:
    state: "yes"
    last_update: "2026-01-18"
  oeis: ["possible"]
  tags: ["graph theory", "ramsey theory"]

- number: "1106"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-11-17"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-11-17"
  formalized:
    state: "yes"
    last_update: "2025-12-10"
  oeis: ["A194259", "A194260"]
  tags: ["number theory"]

- number: "1107"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-11-17"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-11-17"
  formalized:
    state: "yes"
    last_update: "2025-12-04"
  oeis: ["A056828", "A392342", "A392343", "possible"]
  tags: ["number theory", "powerful"]

- number: "1108"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-11-17"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-11-17"
  formalized:
    state: "yes"
    last_update: "2025-12-10"
  oeis: ["A051761", "A115645", "A025494"]
  tags: ["number theory", "factorials"]

- number: "1109"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-12-03"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-12-03"
  formalized:
    state: "yes"
    last_update: "2026-08-08"
  oeis: ["A392164", "A392165"]
  tags: ["number theory"]

- number: "1110"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-12-07"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-12-07"
  formalized:
    state: "yes"
    last_update: "2026-08-03"
  oeis: ["possible"]
  tags: ["number theory"]

- number: "1111"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-12-07"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-12-07"
  formalized:
    state: "no"
    last_update: "2025-09-28"
  oeis: ["possible"]
  tags: ["graph theory"]

- number: "1112"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-12-28"
  formal_status:
    state: "Lean"
    last_update: "2026-07-25"
    url: "https://github.com/beetree/math_erdos_1112"
  status:
    state: "open (Lean)"
    last_update: "2026-07-25"
  formalized:
    state: "no"
    last_update: "2025-09-28"
  oeis: ["N/A"]
  tags: ["additive combinatorics"]

- number: "1113"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-12-28"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-12-28"
  formalized:
    state: "yes"
    last_update: "2026-04-10"
  comments: "Sierpinski numbers"
  oeis: ["A076336"]
  tags: ["number theory", "covering systems"]

- number: "1114"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-12-29"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-12-29"
  formalized:
    state: "no"
    last_update: "2025-09-28"
  oeis: ["N/A"]
  tags: ["analysis", "polynomials"]

- number: "1115"
  prize: "no"
  informal_status:
    state: "solved"
    last_update: "2025-12-29"
  formal_status:
    state: "unformalized"
  status:
    state: "solved"
    last_update: "2025-12-29"
  formalized:
    state: "no"
    last_update: "2025-09-28"
  oeis: ["N/A"]
  tags: ["analysis"]

- number: "1116"
  prize: "no"
  informal_status:
    state: "solved"
    last_update: "2025-12-29"
  formal_status:
    state: "unformalized"
  status:
    state: "solved"
    last_update: "2025-12-29"
  formalized:
    state: "no"
    last_update: "2025-09-28"
  oeis: ["N/A"]
  tags: ["analysis"]

- number: "1117"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-12-29"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-12-29"
  formalized:
    state: "no"
    last_update: "2025-09-28"
  oeis: ["N/A"]
  tags: ["analysis"]

- number: "1118"
  prize: "no"
  informal_status:
    state: "solved"
    last_update: "2025-12-29"
  formal_status:
    state: "unformalized"
  status:
    state: "solved"
    last_update: "2025-12-29"
  formalized:
    state: "no"
    last_update: "2025-09-28"
  oeis: ["N/A"]
  tags: ["analysis"]

- number: "1119"
  prize: "no"
  informal_status:
    state: "independent"
    last_update: "2025-12-30"
  formal_status:
    state: "unformalized"
  status:
    state: "independent"
    last_update: "2025-12-30"
  formalized:
    state: "yes"
    last_update: "2026-06-21"
  oeis: ["N/A"]
  tags: ["analysis", "set theory"]

- number: "1120"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-12-29"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-12-29"
  formalized:
    state: "no"
    last_update: "2025-09-28"
  oeis: ["N/A"]
  tags: ["analysis"]

- number: "1121"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2026-04-19"
  formal_status:
    state: "Lean"
    last_update: "2026-04-19"
  status:
    state: "proved (Lean)"
    last_update: "2026-04-19"
  formalized:
    state: "yes"
    last_update: "2026-08-04"
  oeis: ["N/A"]
  tags: ["geometry"]

- number: "1122"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2025-12-30"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2025-12-30"
  formalized:
    state: "no"
    last_update: "2025-12-30"
  oeis: ["N/A"]
  tags: ["number theory"]

- number: "1123"
  prize: "$100"
  informal_status:
    state: "independent"
    last_update: "2026-01-31"
  formal_status:
    state: "unformalized"
  status:
    state: "independent"
    last_update: "2026-01-31"
  formalized:
    state: "no"
    last_update: "2025-12-30"
  oeis: ["N/A"]
  tags: ["algebra"]

- number: "1124"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2025-12-30"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2025-12-30"
  formalized:
    state: "no"
    last_update: "2025-12-30"
  oeis: ["N/A"]
  tags: ["geometry"]

- number: "1125"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2026-04-11"
  formal_status:
    state: "Lean"
    last_update: "2026-04-11"
  status:
    state: "proved (Lean)"
    last_update: "2026-04-11"
  formalized:
    state: "yes"
    last_update: "2026-06-26"
  oeis: ["N/A"]
  tags: ["analysis"]

- number: "1126"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2026-02-27"
  formal_status:
    state: "Lean"
    last_update: "2026-02-27"
  status:
    state: "proved (Lean)"
    last_update: "2026-02-27"
  formalized:
    state: "yes"
    last_update: "2026-06-26"
  oeis: ["N/A"]
  tags: ["analysis"]

- number: "1127"
  prize: "no"
  informal_status:
    state: "independent"
    last_update: "2025-12-30"
  formal_status:
    state: "unformalized"
  status:
    state: "independent"
    last_update: "2025-12-30"
  formalized:
    state: "no"
    last_update: "2025-12-30"
  oeis: ["N/A"]
  tags: ["geometry", "distances", "set theory"]

- number: "1128"
  prize: "$50"
  informal_status:
    state: "disproved"
    last_update: "2025-12-30"
  formal_status:
    state: "unformalized"
  status:
    state: "disproved"
    last_update: "2025-12-30"
  formalized:
    state: "yes"
    last_update: "2026-06-07"
  oeis: ["N/A"]
  tags: ["set theory", "ramsey theory", "hypergraphs"]

- number: "1129"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2026-01-17"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2026-01-17"
  formalized:
    state: "no"
    last_update: "2026-01-01"
  oeis: ["N/A"]
  tags: ["analysis", "polynomials"]

- number: "1130"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2026-01-17"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2026-01-17"
  formalized:
    state: "no"
    last_update: "2026-01-01"
  oeis: ["N/A"]
  tags: ["analysis", "polynomials"]

- number: "1131"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2026-01-01"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2026-01-01"
  formalized:
    state: "no"
    last_update: "2026-01-01"
  oeis: ["N/A"]
  tags: ["analysis", "polynomials"]

- number: "1132"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2026-01-01"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2026-01-01"
  formalized:
    state: "no"
    last_update: "2026-01-01"
  oeis: ["N/A"]
  tags: ["analysis", "polynomials"]

- number: "1133"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2026-01-01"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2026-01-01"
  formalized:
    state: "yes"
    last_update: "2026-06-08"
  oeis: ["N/A"]
  tags: ["analysis", "polynomials"]

- number: "1134"
  prize: "£10"
  informal_status:
    state: "disproved"
    last_update: "2026-06-21"
  formal_status:
    state: "Lean"
    last_update: "2026-06-21"
  status:
    state: "disproved (Lean)"
    last_update: "2026-06-21"
  formalized:
    state: "no"
    last_update: "2026-01-11"
  oeis: ["A185661"]
  tags: ["number theory"]

- number: "1135"
  prize: "$500"
  informal_status:
    state: "open"
    last_update: "2026-01-11"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2026-01-11"
  formalized:
    state: "yes"
    last_update: "2026-01-13"
  oeis: ["A006370", "A008908"]
  comments: "Collatz conjecture"
  tags: ["number theory"]

- number: "1136"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2026-04-19"
  formal_status:
    state: "Lean"
    last_update: "2026-04-19"
  status:
    state: "proved (Lean)"
    last_update: "2026-04-19"
  formalized:
    state: "yes"
    last_update: "2026-08-04"
  oeis: ["N/A"]
  tags: ["number theory"]

- number: "1137"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2026-01-23"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2026-01-23"
  formalized:
    state: "yes"
    last_update: "2026-01-26"
  oeis: ["A083550", "A005250"]
  tags: ["number theory", "primes"]

- number: "1138"
  prize: "no"
  informal_status:
    state: "disproved"
    last_update: "2026-05-11"
  formal_status:
    state: "Lean"
    last_update: "2026-05-11"
  status:
    state: "disproved (Lean)"
    last_update: "2026-05-11"
  formalized:
    state: "yes"
    last_update: "2026-06-23"
  oeis: ["possible"]
  tags: ["number theory", "primes"]

- number: "1139"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2026-01-23"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2026-01-23"
  formalized:
    state: "yes"
    last_update: "2026-01-28"
  oeis: ["A037143", "A101041"]
  tags: ["number theory", "primes"]

- number: "1140"
  prize: "no"
  informal_status:
    state: "disproved"
    last_update: "2026-01-24"
  formal_status:
    state: "unformalized"
  status:
    state: "disproved"
    last_update: "2026-01-24"
  formalized:
    state: "no"
    last_update: "2026-01-23"
  oeis: ["possible"]
  tags: ["number theory"]

- number: "1141"
  prize: "no"
  informal_status:
    state: "disproved"
    last_update: "2026-04-11"
  formal_status:
    state: "Lean"
    last_update: "2026-04-11"
  status:
    state: "disproved (Lean)"
    last_update: "2026-04-11"
  formalized:
    state: "yes"
    last_update: "2026-02-11"
  oeis: ["A214583"]
  tags: ["number theory", "primes"]

- number: "1142"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2026-01-23"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2026-01-23"
  formalized:
    state: "yes"
    last_update: "2026-02-23"
  oeis: ["A039669"]
  tags: ["number theory", "primes"]

- number: "1143"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2026-01-23"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2026-01-23"
  formalized:
    state: "no"
    last_update: "2026-01-23"
  oeis: ["N/A"]
  tags: ["number theory", "primes"]

- number: "1144"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2026-01-23"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2026-01-23"
  formalized:
    state: "no"
    last_update: "2026-01-23"
  oeis: ["N/A"]
  tags: ["number theory", "probability"]

- number: "1145"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2026-01-23"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2026-01-23"
  formalized:
    state: "yes"
    last_update: "2026-02-09"
  oeis: ["N/A"]
  tags: ["additive combinatorics", "additive basis"]

- number: "1146"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2026-01-23"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2026-01-23"
  formalized:
    state: "yes"
    last_update: "2026-06-08"
  oeis: ["possible"]
  tags: ["number theory"]

- number: "1147"
  prize: "no"
  informal_status:
    state: "disproved"
    last_update: "2026-01-27"
  formal_status:
    state: "unformalized"
  status:
    state: "disproved"
    last_update: "2026-01-27"
  formalized:
    state: "no"
    last_update: "2026-01-23"
  oeis: ["N/A"]
  tags: ["irrational", "additive basis"]

- number: "1148"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2026-03-17"
  formal_status:
    state: "Lean"
    last_update: "2026-03-17"
  status:
    state: "proved (Lean)"
    last_update: "2026-03-17"
  formalized:
    state: "yes"
    last_update: "2026-02-01"
  oeis: ["A390380", "A393168"]
  tags: ["number theory"]

- number: "1149"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2026-01-23"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2026-01-23"
  formalized:
    state: "no"
    last_update: "2026-01-23"
  oeis: ["N/A"]
  tags: ["number theory"]

- number: "1150"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2026-01-23"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2026-01-23"
  formalized:
    state: "yes"
    last_update: "2026-02-06"
  oeis: ["N/A"]
  tags: ["analysis", "polynomials"]

- number: "1151"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2026-01-23"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2026-01-23"
  formalized:
    state: "no"
    last_update: "2026-01-23"
  oeis: ["N/A"]
  tags: ["analysis", "polynomials"]

- number: "1152"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2026-01-23"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2026-01-23"
  formalized:
    state: "no"
    last_update: "2026-01-23"
  oeis: ["N/A"]
  tags: ["analysis", "polynomials"]

- number: "1153"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2026-02-27"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2026-02-27"
  formalized:
    state: "no"
    last_update: "2026-01-23"
  oeis: ["N/A"]
  tags: ["analysis", "polynomials"]

- number: "1154"
  prize: "no"
  informal_status:
    state: "not disprovable"
    last_update: "2026-01-24"
  formal_status:
    state: "unformalized"
  status:
    state: "not disprovable"
    last_update: "2026-01-24"
  formalized:
    state: "no"
    last_update: "2026-01-23"
  oeis: ["N/A"]
  tags: ["analysis"]

- number: "1155"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2026-01-23"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2026-01-23"
  formalized:
    state: "no"
    last_update: "2026-01-23"
  oeis: ["N/A"]
  tags: ["graph theory"]

- number: "1156"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2026-01-23"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2026-01-23"
  formalized:
    state: "no"
    last_update: "2026-01-23"
  oeis: ["N/A"]
  tags: ["graph theory", "chromatic number"]

- number: "1157"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2026-01-23"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2026-01-23"
  formalized:
    state: "no"
    last_update: "2026-01-23"
  oeis: ["possible"]
  tags: ["hypergraphs", "turan number"]

- number: "1158"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2026-01-23"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2026-01-23"
  formalized:
    state: "no"
    last_update: "2026-01-23"
  oeis: ["possible"]
  tags: ["hypergraphs", "turan number"]

- number: "1159"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2026-01-23"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2026-01-23"
  formalized:
    state: "no"
    last_update: "2026-01-23"
  oeis: ["N/A"]
  tags: ["combinatorics"]

- number: "1160"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2026-01-23"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2026-01-23"
  formalized:
    state: "no"
    last_update: "2026-01-23"
  oeis: ["A000001"]
  tags: ["group theory"]

- number: "1161"
  prize: "no"
  informal_status:
    state: "solved"
    last_update: "2026-01-26"
  formal_status:
    state: "unformalized"
  status:
    state: "solved"
    last_update: "2026-01-26"
  formalized:
    state: "no"
    last_update: "2026-01-23"
  oeis: ["possible"]
  tags: ["group theory"]

- number: "1162"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2026-01-23"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2026-01-23"
  formalized:
    state: "no"
    last_update: "2026-01-23"
  oeis: ["possible"]
  tags: ["group theory"]

- number: "1163"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2026-01-23"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2026-01-23"
  formalized:
    state: "no"
    last_update: "2026-01-23"
  oeis: ["N/A"]
  comments: "ambiguous statement"
  tags: ["group theory"]

- number: "1164"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2026-01-23"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2026-01-23"
  formalized:
    state: "no"
    last_update: "2026-01-23"
  oeis: ["N/A"]
  tags: ["probability"]

- number: "1165"
  prize: "no"
  informal_status:
    state: "solved"
    last_update: "2026-01-23"
  formal_status:
    state: "unformalized"
  status:
    state: "solved"
    last_update: "2026-01-23"
  formalized:
    state: "no"
    last_update: "2026-01-23"
  oeis: ["N/A"]
  tags: ["probability"]

- number: "1166"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2026-01-23"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2026-01-23"
  formalized:
    state: "no"
    last_update: "2026-01-23"
  oeis: ["possible"]
  tags: ["probability"]

- number: "1167"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2026-01-23"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2026-01-23"
  formalized:
    state: "yes"
    last_update: "2026-05-25"
  oeis: ["N/A"]
  tags: ["set theory", "probability"]

- number: "1168"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2026-01-23"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2026-01-23"
  formalized:
    state: "no"
    last_update: "2026-01-23"
  oeis: ["N/A"]
  tags: ["set theory", "ramsey theory"]

- number: "1169"
  prize: "no"
  informal_status:
    state: "not disprovable"
    last_update: "2026-01-24"
  formal_status:
    state: "unformalized"
  status:
    state: "not disprovable"
    last_update: "2026-01-24"
  formalized:
    state: "no"
    last_update: "2026-01-23"
  oeis: ["N/A"]
  tags: ["set theory", "ramsey theory"]

- number: "1170"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2026-01-23"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2026-01-23"
  formalized:
    state: "no"
    last_update: "2026-01-23"
  oeis: ["N/A"]
  tags: ["set theory", "ramsey theory"]

- number: "1171"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2026-01-23"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2026-01-23"
  formalized:
    state: "no"
    last_update: "2026-01-23"
  oeis: ["N/A"]
  tags: ["set theory", "ramsey theory"]

- number: "1172"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2026-01-23"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2026-01-23"
  formalized:
    state: "no"
    last_update: "2026-01-23"
  oeis: ["N/A"]
  tags: ["set theory", "ramsey theory"]

- number: "1173"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2026-01-23"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2026-01-23"
  formalized:
    state: "no"
    last_update: "2026-01-23"
  oeis: ["N/A"]
  tags: ["set theory", "combinatorics"]

- number: "1174"
  prize: "no"
  informal_status:
    state: "not disprovable"
    last_update: "2026-03-19"
  formal_status:
    state: "unformalized"
  status:
    state: "not disprovable"
    last_update: "2026-03-19"
  formalized:
    state: "no"
    last_update: "2026-01-23"
  oeis: ["N/A"]
  tags: ["set theory", "ramsey theory"]

- number: "1175"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2026-01-23"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2026-01-23"
  formalized:
    state: "yes"
    last_update: "2026-05-26"
  oeis: ["N/A"]
  tags: ["set theory", "chromatic number"]

- number: "1176"
  prize: "no"
  informal_status:
    state: "not disprovable"
    last_update: "2026-03-18"
  formal_status:
    state: "unformalized"
  status:
    state: "not disprovable"
    last_update: "2026-03-18"
  formalized:
    state: "yes"
    last_update: "2026-02-03"
  oeis: ["N/A"]
  tags: ["set theory", "chromatic number"]

- number: "1177"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2026-01-23"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2026-01-23"
  formalized:
    state: "no"
    last_update: "2026-01-23"
  oeis: ["N/A"]
  tags: ["set theory", "chromatic number", "hypergraphs"]

- number: "1178"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2026-01-25"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2026-01-25"
  formalized:
    state: "no"
    last_update: "2026-01-25"
  oeis: ["N/A"]
  tags: ["graph theory", "hypergraphs"]

- number: "1179"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2026-01-26"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2026-01-26"
  formalized:
    state: "no"
    last_update: "2026-01-25"
  oeis: ["N/A"]
  tags: ["additive combinatorics", "probability"]

- number: "1180"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2026-03-06"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2026-03-06"
  formalized:
    state: "no"
    last_update: "2026-03-06"
  oeis: ["N/A"]
  tags: ["number theory"]

- number: "1181"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2026-03-07"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2026-03-07"
  formalized:
    state: "no"
    last_update: "2026-03-07"
  oeis: ["possible"]
  tags: ["number theory"]

- number: "1182"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2026-03-07"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2026-03-07"
  formalized:
    state: "no"
    last_update: "2026-03-07"
  oeis: ["possible"]
  tags: ["graph theory", "ramsey theory"]

- number: "1183"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2026-03-07"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2026-03-07"
  formalized:
    state: "no"
    last_update: "2026-03-07"
  oeis: ["possible"]
  tags: ["combinatorics", "ramsey theory"]

- number: "1184"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2026-04-04"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2026-04-04"
  formalized:
    state: "no"
    last_update: "2026-04-04"
  oeis: ["possible"]
  tags: ["number theory", "primes"]

- number: "1185"
  prize: "no"
  informal_status:
    state: "solved"
    last_update: "2026-04-04"
  formal_status:
    state: "unformalized"
  status:
    state: "solved"
    last_update: "2026-04-04"
  formalized:
    state: "no"
    last_update: "2026-04-04"
  oeis: ["N/A"]
  tags: ["additive combinatorics", "arithmetic progressions"]

- number: "1186"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2026-04-04"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2026-04-04"
  formalized:
    state: "no"
    last_update: "2026-04-04"
  oeis: ["possible"]
  tags: ["additive combinatorics", "arithmetic progressions"]

- number: "1187"
  prize: "no"
  informal_status:
    state: "solved"
    last_update: "2026-04-04"
  formal_status:
    state: "unformalized"
  status:
    state: "solved"
    last_update: "2026-04-04"
  formalized:
    state: "no"
    last_update: "2026-04-04"
  oeis: ["N/A"]
  tags: ["number theory", "primes", "additive combinatorics", "arithmetic progressions"]

- number: "1188"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2026-04-04"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2026-04-04"
  formalized:
    state: "yes"
    last_update: "2026-08-07"
  oeis: ["possible"]
  tags: ["number theory", "covering systems"]

- number: "1189"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2026-04-04"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2026-04-04"
  formalized:
    state: "no"
    last_update: "2026-04-04"
  oeis: ["possible"]
  tags: ["number theory", "covering systems"]

- number: "1190"
  prize: "no"
  informal_status:
    state: "solved"
    last_update: "2026-05-14"
  formal_status:
    state: "Lean"
    last_update: "2026-05-14"
  status:
    state: "solved (Lean)"
    last_update: "2026-05-14"
  formalized:
    state: "yes"
    last_update: "2026-08-04"
  oeis: ["possible"]
  tags: ["number theory", "covering systems"]

- number: "1191"
  prize: "$1000"
  informal_status:
    state: "open"
    last_update: "2026-04-04"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2026-04-04"
  formalized:
    state: "no"
    last_update: "2026-04-04"
  oeis: ["possible"]
  tags: ["additive combinatorics", "sidon sets"]

- number: "1192"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2026-04-04"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2026-04-04"
  formalized:
    state: "yes"
    last_update: "2026-06-15"
  oeis: ["possible"]
  tags: ["additive combinatorics", "additive basis"]

- number: "1193"
  prize: "no"
  informal_status:
    state: "solved"
    last_update: "2026-04-13"
  formal_status:
    state: "Lean"
    last_update: "2026-04-13"
  status:
    state: "solved (Lean)"
    last_update: "2026-04-13"
  formalized:
    state: "yes"
    last_update: "2026-08-04"
  oeis: ["N/A"]
  tags: ["additive combinatorics"]

- number: "1194"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2026-04-04"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2026-04-04"
  formalized:
    state: "no"
    last_update: "2026-04-04"
  oeis: ["possible"]
  tags: ["additive combinatorics", "additive basis", "sidon sets"]

- number: "1195"
  prize: "no"
  informal_status:
    state: "solved"
    last_update: "2026-04-28"
  formal_status:
    state: "unformalized"
  status:
    state: "solved"
    last_update: "2026-04-28"
  formalized:
    state: "no"
    last_update: "2026-04-04"
  oeis: ["possible"]
  tags: ["number theory"]

- number: "1196"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2026-04-16"
  formal_status:
    state: "Lean"
    last_update: "2026-04-16"
  status:
    state: "proved (Lean)"
    last_update: "2026-04-16"
  formalized:
    state: "yes"
    last_update: "2026-04-15"
  oeis: ["possible"]
  tags: ["number theory", "primitive sets"]

- number: "1197"
  prize: "no"
  informal_status:
    state: "disproved"
    last_update: "2026-04-15"
  formal_status:
    state: "Lean"
    last_update: "2026-04-15"
  status:
    state: "disproved (Lean)"
    last_update: "2026-04-15"
  formalized:
    state: "no"
    last_update: "2026-04-04"
  oeis: ["N/A"]
  tags: ["analysis"]

- number: "1198"
  prize: "no"
  informal_status:
    state: "disproved"
    last_update: "2026-04-24"
  formal_status:
    state: "unformalized"
  status:
    state: "disproved"
    last_update: "2026-04-24"
  formalized:
    state: "no"
    last_update: "2026-04-04"
  oeis: ["N/A"]
  tags: ["additive combinatorics", "ramsey theory"]

- number: "1199"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2026-04-04"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2026-04-04"
  formalized:
    state: "yes"
    last_update: "2026-05-04"
  oeis: ["possible"]
  tags: ["additive combinatorics", "ramsey theory"]

- number: "1200"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2026-04-04"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2026-04-04"
  formalized:
    state: "no"
    last_update: "2026-04-04"
  oeis: ["possible"]
  tags: ["number theory", "primes"]

- number: "1201"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2026-04-04"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2026-04-04"
  formalized:
    state: "yes"
    last_update: "2026-06-07"
  oeis: ["possible"]
  tags: ["number theory", "primes"]

- number: "1202"
  prize: "no"
  informal_status:
    state: "solved"
    last_update: "2026-04-04"
  formal_status:
    state: "unformalized"
  status:
    state: "solved"
    last_update: "2026-04-04"
  formalized:
    state: "no"
    last_update: "2026-04-04"
  oeis: ["possible"]
  tags: ["number theory", "primes"]

- number: "1203"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2026-04-04"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2026-04-04"
  formalized:
    state: "yes"
    last_update: "2026-05-12"
  oeis: ["possible"]
  tags: ["number theory"]

- number: "1204"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2026-04-04"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2026-04-04"
  formalized:
    state: "no"
    last_update: "2026-04-04"
  oeis: ["A008407", "A023193", "A135311", "possible"]
  tags: ["number theory"]

- number: "1205"
  prize: "no"
  informal_status:
    state: "solved"
    last_update: "2026-04-04"
  formal_status:
    state: "unformalized"
  status:
    state: "solved"
    last_update: "2026-04-04"
  formalized:
    state: "no"
    last_update: "2026-04-04"
  oeis: ["possible"]
  tags: ["number theory"]

- number: "1206"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2026-04-04"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2026-04-04"
  formalized:
    state: "no"
    last_update: "2026-04-04"
  oeis: ["possible"]
  tags: ["number theory", "sidon sets"]

- number: "1207"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2026-04-04"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2026-04-04"
  formalized:
    state: "no"
    last_update: "2026-04-04"
  oeis: ["possible"]
  tags: ["geometry", "distances"]

- number: "1208"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2026-04-04"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2026-04-04"
  formalized:
    state: "no"
    last_update: "2026-04-04"
  oeis: ["A193838", "A271490", "possible"]
  tags: ["geometry", "distances"]

- number: "1209"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2026-04-04"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2026-04-04"
  formalized:
    state: "yes"
    last_update: "2026-06-07"
  oeis: ["possible"]
  tags: ["number theory"]

- number: "1210"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2026-04-04"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2026-04-04"
  formalized:
    state: "yes"
    last_update: "2026-05-03"
  oeis: ["possible"]
  tags: ["number theory"]

- number: "1211"
  prize: "no"
  informal_status:
    state: "solved"
    last_update: "2026-04-04"
  formal_status:
    state: "unformalized"
  status:
    state: "solved"
    last_update: "2026-04-04"
  formalized:
    state: "no"
    last_update: "2026-04-04"
  oeis: ["possible"]
  tags: ["number theory", "ramsey theory"]

- number: "1212"
  prize: "no"
  informal_status:
    state: "open"
    last_update: "2026-04-04"
  formal_status:
    state: "unformalized"
  status:
    state: "open"
    last_update: "2026-04-04"
  formalized:
    state: "yes"
    last_update: "2026-06-24"
  oeis: ["possible"]
  tags: ["number theory", "primes"]

- number: "1213"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2026-04-21"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2026-04-21"
  formalized:
    state: "no"
    last_update: "2026-04-04"
  oeis: ["possible"]
  tags: ["additive combinatorics"]

- number: "1214"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2026-04-21"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2026-04-21"
  formalized:
    state: "yes"
    last_update: "2026-05-26"
  oeis: ["N/A"]
  tags: ["number theory"]

- number: "1215"
  prize: "no"
  informal_status:
    state: "disproved"
    last_update: "2026-04-21"
  formal_status:
    state: "unformalized"
  status:
    state: "disproved"
    last_update: "2026-04-21"
  formalized:
    state: "no"
    last_update: "2026-04-04"
  oeis: ["N/A"]
  tags: ["analysis"]

- number: "1216"
  prize: "no"
  informal_status:
    state: "disproved"
    last_update: "2026-04-21"
  formal_status:
    state: "unformalized"
  status:
    state: "disproved"
    last_update: "2026-04-21"
  formalized:
    state: "no"
    last_update: "2026-04-04"
  oeis: ["possible"]
  tags: ["graph theory", "ramsey theory"]

- number: "1217"
  prize: "no"
  informal_status:
    state: "proved"
    last_update: "2026-04-21"
  formal_status:
    state: "unformalized"
  status:
    state: "proved"
    last_update: "2026-04-21"
  formalized:
    state: "no"
    last_update: "2026-04-04"
  oeis: ["N/A"]
  tags: ["number theory", "divisors", "primitive sets"]