euler50.ipynb

   1 {
   2  "cells": [
   3   {
   4    "cell_type": "code",
   5    "execution_count": 1,
   6    "metadata": {
   7     "collapsed": false,
   8     "scrolled": true
   9    },
  10    "outputs": [
  11     {
  12      "data": {
  13       "text/plain": [
  14        "104743"
  15       ]
  16      },
  17      "execution_count": 1,
  18      "metadata": {},
  19      "output_type": "execute_result"
  20     }
  21    ],
  22    "source": [
  23     "load 'primes.rb'\n",
  24     "$primes = Primes.instance\n",
  25     "$primes[10000]   # returns the 10,001st prime"
  26    ]
  27   },
  28   {
  29    "cell_type": "code",
  30    "execution_count": 2,
  31    "metadata": {
  32     "collapsed": false
  33    },
  34    "outputs": [
  35     {
  36      "data": {
  37       "text/plain": [
  38        "[2, 3, 5]"
  39       ]
  40      },
  41      "execution_count": 2,
  42      "metadata": {},
  43      "output_type": "execute_result"
  44     }
  45    ],
  46    "source": [
  47     "(0...(0+3)).map{|i| $primes[i]}"
  48    ]
  49   },
  50   {
  51    "cell_type": "code",
  52    "execution_count": 3,
  53    "metadata": {
  54     "collapsed": false
  55    },
  56    "outputs": [
  57     {
  58      "data": {
  59       "text/plain": [
  60        ":prime_slice"
  61       ]
  62      },
  63      "execution_count": 3,
  64      "metadata": {},
  65      "output_type": "execute_result"
  66     }
  67    ],
  68    "source": [
  69     "def prime_slice(start, len)\n",
  70     "  (start...(start + len)).map{|i| $primes[i]}\n",
  71     "end"
  72    ]
  73   },
  74   {
  75    "cell_type": "code",
  76    "execution_count": 4,
  77    "metadata": {
  78     "collapsed": false
  79    },
  80    "outputs": [
  81     {
  82      "data": {
  83       "text/plain": [
  84        ":sum_primes"
  85       ]
  86      },
  87      "execution_count": 4,
  88      "metadata": {},
  89      "output_type": "execute_result"
  90     }
  91    ],
  92    "source": [
  93     "def sum_primes(start, len)\n",
  94     "  prime_slice(start, len).sum\n",
  95     "end"
  96    ]
  97   },
  98   {
  99    "cell_type": "code",
 100    "execution_count": 5,
 101    "metadata": {
 102     "collapsed": false
 103    },
 104    "outputs": [
 105     {
 106      "data": {
 107       "text/plain": [
 108        "[2, 3, 5, 7, 11]"
 109       ]
 110      },
 111      "execution_count": 5,
 112      "metadata": {},
 113      "output_type": "execute_result"
 114     }
 115    ],
 116    "source": [
 117     "prime_slice(0, 5)"
 118    ]
 119   },
 120   {
 121    "cell_type": "code",
 122    "execution_count": 6,
 123    "metadata": {
 124     "collapsed": false
 125    },
 126    "outputs": [
 127     {
 128      "data": {
 129       "text/plain": [
 130        "28"
 131       ]
 132      },
 133      "execution_count": 6,
 134      "metadata": {},
 135      "output_type": "execute_result"
 136     }
 137    ],
 138    "source": [
 139     "sum_primes(0, 5)"
 140    ]
 141   },
 142   {
 143    "cell_type": "code",
 144    "execution_count": 8,
 145    "metadata": {
 146     "collapsed": false,
 147     "scrolled": true
 148    },
 149    "outputs": [
 150     {
 151      "data": {
 152       "text/plain": [
 153        "[3, 543, 997651]"
 154       ]
 155      },
 156      "execution_count": 8,
 157      "metadata": {},
 158      "output_type": "execute_result"
 159     }
 160    ],
 161    "source": [
 162     "sum_limit = 10**6\n",
 163     "\n",
 164     "start = 0\n",
 165     "best_start = 0\n",
 166     "best_length = 1\n",
 167     "while $primes[start] <= sum_limit\n",
 168     "  # puts start\n",
 169     "  length = 1\n",
 170     "  sp = sum_primes(start, length)\n",
 171     "  while sp <= sum_limit\n",
 172     "    if sp.prime? && length > best_length\n",
 173     "      best_start = start\n",
 174     "      best_length = length\n",
 175     "      # puts \"#{start} - #{length} : #{sum_primes(start, length)}\"\n",
 176     "    end\n",
 177     "    length += 1\n",
 178     "    sp = sum_primes(start, length)\n",
 179     "  end\n",
 180     "  start += 1\n",
 181     "end\n",
 182     "[best_start, best_length, sum_primes(best_start, best_length)]"
 183    ]
 184   },
 185   {
 186    "cell_type": "code",
 187    "execution_count": null,
 188    "metadata": {
 189     "collapsed": true
 190    },
 191    "outputs": [],
 192    "source": []
 193   }
 194  ],
 195  "metadata": {
 196   "kernelspec": {
 197    "display_name": "Ruby 2.4.0",
 198    "language": "ruby",
 199    "name": "ruby"
 200   },
 201   "language_info": {
 202    "file_extension": ".rb",
 203    "mimetype": "application/x-ruby",
 204    "name": "ruby",
 205    "version": "2.4.0"
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 207  },
 208  "nbformat": 4,
 209  "nbformat_minor": 0
 210 }