euler37.ipynb

   1 {
   2  "cells": [
   3   {
   4    "cell_type": "code",
   5    "execution_count": 1,
   6    "metadata": {
   7     "collapsed": false
   8    },
   9    "outputs": [
  10     {
  11      "data": {
  12       "text/plain": [
  13        "true"
  14       ]
  15      },
  16      "execution_count": 1,
  17      "metadata": {},
  18      "output_type": "execute_result"
  19     }
  20    ],
  21    "source": [
  22     "load 'primes.rb'\n",
  23     "load 'array-numbers.rb'"
  24    ]
  25   },
  26   {
  27    "cell_type": "code",
  28    "execution_count": 4,
  29    "metadata": {
  30     "collapsed": false
  31    },
  32    "outputs": [
  33     {
  34      "data": {
  35       "text/plain": [
  36        ":truncations"
  37       ]
  38      },
  39      "execution_count": 4,
  40      "metadata": {},
  41      "output_type": "execute_result"
  42     }
  43    ],
  44    "source": [
  45     "def truncations(n)\n",
  46     "  ds = n.to_digits\n",
  47     "  dsl = ds.length\n",
  48     "  (0...(dsl-1)).flat_map {|i| [ds[0..i].to_i, ds[(i+1)..dsl].to_i]}\n",
  49     "end"
  50    ]
  51   },
  52   {
  53    "cell_type": "code",
  54    "execution_count": 5,
  55    "metadata": {
  56     "collapsed": false
  57    },
  58    "outputs": [
  59     {
  60      "data": {
  61       "text/plain": [
  62        "[1, 23, 12, 3]"
  63       ]
  64      },
  65      "execution_count": 5,
  66      "metadata": {},
  67      "output_type": "execute_result"
  68     }
  69    ],
  70    "source": [
  71     "truncations(123)"
  72    ]
  73   },
  74   {
  75    "cell_type": "code",
  76    "execution_count": 6,
  77    "metadata": {
  78     "collapsed": false
  79    },
  80    "outputs": [
  81     {
  82      "data": {
  83       "text/plain": [
  84        ":truncatable_prime"
  85       ]
  86      },
  87      "execution_count": 6,
  88      "metadata": {},
  89      "output_type": "execute_result"
  90     }
  91    ],
  92    "source": [
  93     "def truncatable_prime(n)\n",
  94     "  n.prime? && truncations(n).all? {|i| i.prime?}\n",
  95     "end"
  96    ]
  97   },
  98   {
  99    "cell_type": "code",
 100    "execution_count": 7,
 101    "metadata": {
 102     "collapsed": false
 103    },
 104    "outputs": [
 105     {
 106      "data": {
 107       "text/plain": [
 108        "true"
 109       ]
 110      },
 111      "execution_count": 7,
 112      "metadata": {},
 113      "output_type": "execute_result"
 114     }
 115    ],
 116    "source": [
 117     "truncatable_prime(3797)"
 118    ]
 119   },
 120   {
 121    "cell_type": "code",
 122    "execution_count": 8,
 123    "metadata": {
 124     "collapsed": false
 125    },
 126    "outputs": [
 127     {
 128      "data": {
 129       "text/plain": [
 130        "false"
 131       ]
 132      },
 133      "execution_count": 8,
 134      "metadata": {},
 135      "output_type": "execute_result"
 136     }
 137    ],
 138    "source": [
 139     "truncatable_prime(3799)"
 140    ]
 141   },
 142   {
 143    "cell_type": "code",
 144    "execution_count": 9,
 145    "metadata": {
 146     "collapsed": false
 147    },
 148    "outputs": [
 149     {
 150      "data": {
 151       "text/plain": [
 152        "[23, 37, 53, 73, 313, 317, 373, 797, 3137, 3797, 739397]"
 153       ]
 154      },
 155      "execution_count": 9,
 156      "metadata": {},
 157      "output_type": "execute_result"
 158     }
 159    ],
 160    "source": [
 161     "(10..(10**6)).select {|n| truncatable_prime(n)}.to_a"
 162    ]
 163   },
 164   {
 165    "cell_type": "code",
 166    "execution_count": 10,
 167    "metadata": {
 168     "collapsed": false
 169    },
 170    "outputs": [
 171     {
 172      "data": {
 173       "text/plain": [
 174        "[23, 37, 53, 73, 313, 317, 373, 797, 3137, 3797, 739397]"
 175       ]
 176      },
 177      "execution_count": 10,
 178      "metadata": {},
 179      "output_type": "execute_result"
 180     }
 181    ],
 182    "source": [
 183     "(10..(10**10)).lazy.select {|n| truncatable_prime(n)}.take(11).to_a"
 184    ]
 185   },
 186   {
 187    "cell_type": "code",
 188    "execution_count": 11,
 189    "metadata": {
 190     "collapsed": false
 191    },
 192    "outputs": [
 193     {
 194      "data": {
 195       "text/plain": [
 196        "748317"
 197       ]
 198      },
 199      "execution_count": 11,
 200      "metadata": {},
 201      "output_type": "execute_result"
 202     }
 203    ],
 204    "source": [
 205     "(10..(10**7)).lazy.select {|n| truncatable_prime(n)}.take(11).sum"
 206    ]
 207   },
 208   {
 209    "cell_type": "code",
 210    "execution_count": null,
 211    "metadata": {
 212     "collapsed": true
 213    },
 214    "outputs": [],
 215    "source": []
 216   }
 217  ],
 218  "metadata": {
 219   "kernelspec": {
 220    "display_name": "Ruby 2.4.0",
 221    "language": "ruby",
 222    "name": "ruby"
 223   },
 224   "language_info": {
 225    "file_extension": ".rb",
 226    "mimetype": "application/x-ruby",
 227    "name": "ruby",
 228    "version": "2.4.0"
 229   }
 230  },
 231  "nbformat": 4,
 232  "nbformat_minor": 0
 233 }