{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Diagonals\n",
    "\n",
    "```\n",
    "37 36 35 34 33 32 31\n",
    "38 17 16 15 14 13 30\n",
    "39 18  5  4  3 12 29\n",
    "40 19  6  1  2 11 28\n",
    "41 20  7  8  9 10 27\n",
    "42 21 22 23 24 25 26\n",
    "43 44 45 46 47 48 49\n",
    "```\n",
    "\n",
    "Down-right goes as 1, 9, 25, 49: (2i+1)^2, starting from i=0\n",
    "\n",
    "Down left goes as 1 7 21 43: (2i+1)^2 - 2i\n",
    "\n",
    "Up left goes 1 5 17 37: (2i + 1)^2 - 4i\n",
    "\n",
    "Up right goes 1 3 13 31: (2i + 1)^2 - 6i\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9973"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "require_relative 'primes'\n",
    "primes = Primes.instance\n",
    "# primes.load_primes \"primes_2000000.txt\"\n",
    "primes.primes.last"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 9, 25, 49, 81]"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(0...5).map {|i| (2 * i + 1) ** 2}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 7, 21, 43, 73]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(0...5).map {|i| (2 * i + 1) ** 2 - 2 * i}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 5, 17, 37, 65]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(0...5).map {|i| (2 * i + 1) ** 2 - 4 * i}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 3, 13, 31, 57]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(0...5).map {|i| (2 * i + 1) ** 2 - 6 * i}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       ":diagonals"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def diagonals(n)\n",
    "  [1] + (1...n).flat_map {|i| [\n",
    "      (2 * i + 1) ** 2,\n",
    "      (2 * i + 1) ** 2 - 2 * i,\n",
    "      (2 * i + 1) ** 2 - 4 * i,\n",
    "      (2 * i + 1) ** 2 - 6 * i\n",
    "      ]}\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       ":diagonal_tips"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def diagonal_tips(n)\n",
    "  [# (2 * n + 1) ** 2,\n",
    "   (2 * n + 1) ** 2 - 2 * n,\n",
    "   (2 * n + 1) ** 2 - 4 * n,\n",
    "   (2 * n + 1) ** 2 - 6 * n]\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 9, 7, 5, 3, 25, 21, 17, 13]"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "diagonals(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "diagonals(3).length"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[7, 5, 3, 17, 13]"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "diagonals(3).select {|n| n.prime?}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "26241"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "l = 1\n",
    "tip_primes = diagonal_tips(l).select {|n| primes.is_prime? n}\n",
    "prime_count = tip_primes.length\n",
    "while prime_count * 10 > (4 * l + 1)\n",
    "  # puts l if l % 500 == 0\n",
    "  l += 1\n",
    "  tip_primes = diagonal_tips(l).select {|n| primes.is_prime? n}\n",
    "  prime_count += tip_primes.length\n",
    "end\n",
    "l * 2 + 1 # side length"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Ruby 2.4.0",
   "language": "ruby",
   "name": "ruby"
  },
  "language_info": {
   "file_extension": ".rb",
   "mimetype": "application/x-ruby",
   "name": "ruby",
   "version": "2.4.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}