Lunar Arithmetic is a variance of arithmetic without carry.

In Lunar Arithmetic, the addition is defined as the max() of digits in an arbitrary base, in this case decimal.

+ 153 
  426
  ---
  456

And, multiplication is defined as the min() of digits, for example: 6 + 7 = 6.

× 153
  426
  ---
  153
 122
143
-----
14253

Lunar Multisets

A different way of looking at lunar's addition and multiplication as union and intersection on a a set where each digit is equal to the count of an item. Lunar primes are numbers irreducible under intersection. Multiplicities are capped at 9 in base-10. The addition operator gives the union, or LCM, of two sets:

+  20
    1
  ---
   21

The intersection, or GCD, of two multisets is reached with the multiplication operator:

×  21
   12
  ---
   11

Unlike Tropical arithmetic, there is no way to increment the number of items in a bag, addition can only raise a digit to a new ceiling.

Lunar Primes

In the usual arithmetic, a prime number is defined as a number whose only possible factorisation is 1 × n. Analogously, in the lunar arithmetic, a prime number is defined as a number whose only factorisation is 9 × n where 9 is the multiplicative identity which corresponds to 1 in usual arithmetic.

19, 29, 39, 49, 59, 69, 79, 89, 90, 91, 92, 93, 94, 95 ..

• Even Numbers(2 × n): 0, 1, 2, 10, 11, 12, 20, 21, 22, 100, 101, 102, 120 ..
• Squre Numbers(n × n): 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 100, 111, 112, 113, 114 ..

incoming: tropical arithmetic 2025