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   "source": [
    "This notebook is used to generate data regarding the Goldbach conjecture: rows are of the form $N, a, b$ where $N$ is an even number, $a< b$ are prime and $N=a + b$.\n",
    "\n",
    "First we write a Python function `goldbach` that takes `N` and returns all pairs of numbers $a, b$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import sympy as sym\n",
    "import pandas as pd\n",
    "\n",
    "def goldbach(N):\n",
    "    \"\"\"Returns all pairs of primes that sum to give N\"\"\"\n",
    "    primes = list(sym.primerange(1, N))\n",
    "    sums = []\n",
    "    for i, p1 in enumerate(primes):\n",
    "        for p2 in primes[i:]:\n",
    "            if p1 + p2 == N:\n",
    "                sums.append((p1, p2))\n",
    "    return sums"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us use the above function to create our data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "maxN = 500\n",
    "data = [[N, *pair] for N in range(4, maxN + 1) \n",
    "        for pair in goldbach(N) if N % 2 == 0 ]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us write our data to an excel file:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.DataFrame(data, columns=[\"N\",\"a\", \"b\"])  # Create a data frame\n",
    "df.to_excel(\"data/goldbach.xlsx\")  # Write it to excel"
   ]
  }
 ],
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