euler50.ipynb

   1 {
   2  "cells": [
   3   {
   4    "cell_type": "code",
   5    "execution_count": 12,
   6    "metadata": {
   7     "collapsed": false,
   8     "scrolled": true
   9    },
  10    "outputs": [
  11     {
  12      "data": {
  13       "text/plain": [
  14        "104743"
  15       ]
  16      },
  17      "execution_count": 12,
  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": 13,
  31    "metadata": {
  32     "collapsed": false
  33    },
  34    "outputs": [
  35     {
  36      "data": {
  37       "text/plain": [
  38        "[2, 3, 5]"
  39       ]
  40      },
  41      "execution_count": 13,
  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": 17,
  53    "metadata": {
  54     "collapsed": false
  55    },
  56    "outputs": [
  57     {
  58      "data": {
  59       "text/plain": [
  60        ":prime_slice"
  61       ]
  62      },
  63      "execution_count": 17,
  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": 18,
  77    "metadata": {
  78     "collapsed": false
  79    },
  80    "outputs": [
  81     {
  82      "data": {
  83       "text/plain": [
  84        ":sum_primes"
  85       ]
  86      },
  87      "execution_count": 18,
  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": 20,
 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": 20,
 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": 19,
 123    "metadata": {
 124     "collapsed": false
 125    },
 126    "outputs": [
 127     {
 128      "data": {
 129       "text/plain": [
 130        "28"
 131       ]
 132      },
 133      "execution_count": 19,
 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": 30,
 145    "metadata": {
 146     "collapsed": false,
 147     "scrolled": true
 148    },
 149    "outputs": [
 150     {
 151      "name": "stdout",
 152      "output_type": "stream",
 153      "text": [
 154       "0 - 2 : 5\n",
 155       "0 - 4 : 17\n",
 156       "0 - 6 : 41\n",
 157       "0 - 12 : 197\n",
 158       "0 - 14 : 281\n",
 159       "0 - 60 : 7699\n",
 160       "0 - 64 : 8893\n",
 161       "0 - 96 : 22039\n",
 162       "0 - 100 : 24133\n",
 163       "0 - 102 : 25237\n",
 164       "0 - 108 : 28697\n",
 165       "0 - 114 : 32353\n",
 166       "0 - 122 : 37561\n",
 167       "0 - 124 : 38921\n",
 168       "0 - 130 : 43201\n",
 169       "0 - 132 : 44683\n",
 170       "0 - 146 : 55837\n",
 171       "0 - 152 : 61027\n",
 172       "0 - 158 : 66463\n",
 173       "0 - 162 : 70241\n",
 174       "0 - 178 : 86453\n",
 175       "0 - 192 : 102001\n",
 176       "0 - 198 : 109147\n",
 177       "0 - 204 : 116533\n",
 178       "0 - 206 : 119069\n",
 179       "0 - 208 : 121631\n",
 180       "0 - 214 : 129419\n",
 181       "0 - 216 : 132059\n",
 182       "0 - 296 : 263171\n",
 183       "0 - 308 : 287137\n",
 184       "0 - 326 : 325019\n",
 185       "0 - 328 : 329401\n",
 186       "0 - 330 : 333821\n",
 187       "0 - 332 : 338279\n",
 188       "0 - 334 : 342761\n",
 189       "0 - 342 : 360979\n",
 190       "0 - 350 : 379667\n",
 191       "0 - 356 : 393961\n",
 192       "0 - 358 : 398771\n",
 193       "0 - 426 : 581921\n",
 194       "0 - 446 : 642869\n",
 195       "0 - 458 : 681257\n",
 196       "0 - 460 : 687767\n",
 197       "0 - 464 : 700897\n",
 198       "0 - 480 : 754573\n",
 199       "0 - 484 : 768373\n",
 200       "0 - 488 : 782263\n",
 201       "0 - 512 : 868151\n",
 202       "0 - 530 : 935507\n",
 203       "0 - 536 : 958577\n",
 204       "2 - 537 : 970219\n",
 205       "2 - 539 : 978037\n",
 206       "3 - 543 : 997651\n"
 207      ]
 208     },
 209     {
 210      "data": {
 211       "text/plain": [
 212        "[3, 543, 997651]"
 213       ]
 214      },
 215      "execution_count": 30,
 216      "metadata": {},
 217      "output_type": "execute_result"
 218     }
 219    ],
 220    "source": [
 221     "sum_limit = 10**6\n",
 222     "\n",
 223     "start = 0\n",
 224     "best_start = 0\n",
 225     "best_length = 1\n",
 226     "while primes[start] <= sum_limit\n",
 227     "  # puts start\n",
 228     "  length = 1\n",
 229     "  sp = sum_primes(start, length)\n",
 230     "  while sp <= sum_limit\n",
 231     "    if sp.prime? && length > best_length\n",
 232     "      best_start = start\n",
 233     "      best_length = length\n",
 234     "      # puts \"#{start} - #{length} : #{sum_primes(start, length)}\"\n",
 235     "    end\n",
 236     "    length += 1\n",
 237     "    sp = sum_primes(start, length)\n",
 238     "  end\n",
 239     "  start += 1\n",
 240     "end\n",
 241     "[best_start, best_length, sum_primes(best_start, best_length)]"
 242    ]
 243   },
 244   {
 245    "cell_type": "code",
 246    "execution_count": null,
 247    "metadata": {
 248     "collapsed": true
 249    },
 250    "outputs": [],
 251    "source": []
 252   }
 253  ],
 254  "metadata": {
 255   "kernelspec": {
 256    "display_name": "Ruby 2.4.0",
 257    "language": "ruby",
 258    "name": "ruby"
 259   },
 260   "language_info": {
 261    "file_extension": ".rb",
 262    "mimetype": "application/x-ruby",
 263    "name": "ruby",
 264    "version": "2.4.0"
 265   }
 266  },
 267  "nbformat": 4,
 268  "nbformat_minor": 0
 269 }