euler35.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        "#<Primes:0x0055fc1b2516c0 @primes=[2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997, 1009, 1013, 1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069, 1087, 1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151, 1153, 1163, 1171, 1181, 1187, 1193, 1201, 1213, 1217, 1223, 1229, 1231, 1237, 1249, 1259, 1277, 1279, 1283, 1289, 1291, 1297, 1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373, 1381, 1399, 1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451, 1453, 1459, 1471, 1481, 1483, 1487, 1489, 1493, 1499, 1511, 1523, 1531, 1543, 1549, 1553, 1559, 1567, 1571, 1579, 1583, 1597, 1601, 1607, 1609, 1613, 1619, 1621, 1627, 1637, 1657, 1663, 1667, 1669, 1693, 1697, 1699, 1709, 1721, 1723, 1733, 1741, 1747, 1753, 1759, 1777, 1783, 1787, 1789, 1801, 1811, 1823, 1831, 1847, 1861, 1867, 1871, 1873, 1877, 1879, 1889, 1901, 1907, 1913, 1931, 1933, 1949, 1951, 1973, 1979, 1987, 1993, 1997, 1999, 2003, 2011, 2017, 2027, 2029, 2039, 2053, 2063, 2069, 2081, 2083, 2087, 2089, 2099, 2111, 2113, 2129, 2131, 2137, 2141, 2143, 2153, 2161, 2179, 2203, 2207, 2213, 2221, 2237, 2239, 2243, 2251, 2267, 2269, 2273, 2281, 2287, 2293, 2297, 2309, 2311, 2333, 2339, 2341, 2347, 2351, 2357, 2371, 2377, 2381, 2383, 2389, 2393, 2399, 2411, 2417, 2423, 2437, 2441, 2447, 2459, 2467, 2473, 2477, 2503, 2521, 2531, 2539, 2543, 2549, 2551, 2557, 2579, 2591, 2593, 2609, 2617, 2621, 2633, 2647, 2657, 2659, 2663, 2671, 2677, 2683, 2687, 2689, 2693, 2699, 2707, 2711, 2713, 2719, 2729, 2731, 2741, 2749, 2753, 2767, 2777, 2789, 2791, 2797, 2801, 2803, 2819, 2833, 2837, 2843, 2851, 2857, 2861, 2879, 2887, 2897, 2903, 2909, 2917, 2927, 2939, 2953, 2957, 2963, 2969, 2971, 2999, 3001, 3011, 3019, 3023, 3037, 3041, 3049, 3061, 3067, 3079, 3083, 3089, 3109, 3119, 3121, 3137, 3163, 3167, 3169, 3181, 3187, 3191, 3203, 3209, 3217, 3221, 3229, 3251, 3253, 3257, 3259, 3271, 3299, 3301, 3307, 3313, 3319, 3323, 3329, 3331, 3343, 3347, 3359, 3361, 3371, 3373, 3389, 3391, 3407, 3413, 3433, 3449, 3457, 3461, 3463, 3467, 3469, 3491, 3499, 3511, 3517, 3527, 3529, 3533, 3539, 3541, 3547, 3557, 3559, 3571, 3581, 3583, 3593, 3607, 3613, 3617, 3623, 3631, 3637, 3643, 3659, 3671, 3673, 3677, 3691, 3697, 3701, 3709, 3719, 3727, 3733, 3739, 3761, 3767, 3769, 3779, 3793, 3797, 3803, 3821, 3823, 3833, 3847, 3851, 3853, 3863, 3877, 3881, 3889, 3907, 3911, 3917, 3919, 3923, 3929, 3931, 3943, 3947, 3967, 3989, 4001, 4003, 4007, 4013, 4019, 4021, 4027, 4049, 4051, 4057, 4073, 4079, 4091, 4093, 4099, 4111, 4127, 4129, 4133, 4139, 4153, 4157, 4159, 4177, 4201, 4211, 4217, 4219, 4229, 4231, 4241, 4243, 4253, 4259, 4261, 4271, 4273, 4283, 4289, 4297, 4327, 4337, 4339, 4349, 4357, 4363, 4373, 4391, 4397, 4409, 4421, 4423, 4441, 4447, 4451, 4457, 4463, 4481, 4483, 4493, 4507, 4513, 4517, 4519, 4523, 4547, 4549, 4561, 4567, 4583, 4591, 4597, 4603, 4621, 4637, 4639, 4643, 4649, 4651, 4657, 4663, 4673, 4679, 4691, 4703, 4721, 4723, 4729, 4733, 4751, 4759, 4783, 4787, 4789, 4793, 4799, 4801, 4813, 4817, 4831, 4861, 4871, 4877, 4889, 4903, 4909, 4919, 4931, 4933, 4937, 4943, 4951, 4957, 4967, 4969, 4973, 4987, 4993, 4999, 5003, 5009, 5011, 5021, 5023, 5039, 5051, 5059, 5077, 5081, 5087, 5099, 5101, 5107, 5113, 5119, 5147, 5153, 5167, 5171, 5179, 5189, 5197, 5209, 5227, 5231, 5233, 5237, 5261, 5273, 5279, 5281, 5297, 5303, 5309, 5323, 5333, 5347, 5351, 5381, 5387, 5393, 5399, 5407, 5413, 5417, 5419, 5431, 5437, 5441, 5443, 5449, 5471, 5477, 5479, 5483, 5501, 5503, 5507, 5519, 5521, 5527, 5531, 5557, 5563, 5569, 5573, 5581, 5591, 5623, 5639, 5641, 5647, 5651, 5653, 5657, 5659, 5669, 5683, 5689, 5693, 5701, 5711, 5717, 5737, 5741, 5743, 5749, 5779, 5783, 5791, 5801, 5807, 5813, 5821, 5827, 5839, 5843, 5849, 5851, 5857, 5861, 5867, 5869, 5879, 5881, 5897, 5903, 5923, 5927, 5939, 5953, 5981, 5987, 6007, 6011, 6029, 6037, 6043, 6047, 6053, 6067, 6073, 6079, 6089, 6091, 6101, 6113, 6121, 6131, 6133, 6143, 6151, 6163, 6173, 6197, 6199, 6203, 6211, 6217, 6221, 6229, 6247, 6257, 6263, 6269, 6271, 6277, 6287, 6299, 6301, 6311, 6317, 6323, 6329, 6337, 6343, 6353, 6359, 6361, 6367, 6373, 6379, 6389, 6397, 6421, 6427, 6449, 6451, 6469, 6473, 6481, 6491, 6521, 6529, 6547, 6551, 6553, 6563, 6569, 6571, 6577, 6581, 6599, 6607, 6619, 6637, 6653, 6659, 6661, 6673, 6679, 6689, 6691, 6701, 6703, 6709, 6719, 6733, 6737, 6761, 6763, 6779, 6781, 6791, 6793, 6803, 6823, 6827, 6829, 6833, 6841, 6857, 6863, 6869, 6871, 6883, 6899, 6907, 6911, 6917, 6947, 6949, 6959, 6961, 6967, 6971, 6977, 6983, 6991, 6997, 7001, 7013, 7019, 7027, 7039, 7043, 7057, 7069, 7079, 7103, 7109, 7121, 7127, 7129, 7151, 7159, 7177, 7187, 7193, 7207, 7211, 7213, 7219, 7229, 7237, 7243, 7247, 7253, 7283, 7297, 7307, 7309, 7321, 7331, 7333, 7349, 7351, 7369, 7393, 7411, 7417, 7433, 7451, 7457, 7459, 7477, 7481, 7487, 7489, 7499, 7507, 7517, 7523, 7529, 7537, 7541, 7547, 7549, 7559, 7561, 7573, 7577, 7583, 7589, 7591, 7603, 7607, 7621, 7639, 7643, 7649, 7669, 7673, 7681, 7687, 7691, 7699, 7703, 7717, 7723, 7727, 7741, 7753, 7757, 7759, 7789, 7793, 7817, 7823, 7829, 7841, 7853, 7867, 7873, 7877, 7879, 7883, 7901, 7907, 7919, 7927, 7933, 7937, 7949, 7951, 7963, 7993, 8009, 8011, 8017, 8039, 8053, 8059, 8069, 8081, 8087, 8089, 8093, 8101, 8111, 8117, 8123, 8147, 8161, 8167, 8171, 8179, 8191, 8209, 8219, 8221, 8231, 8233, 8237, 8243, 8263, 8269, 8273, 8287, 8291, 8293, 8297, 8311, 8317, 8329, 8353, 8363, 8369, 8377, 8387, 8389, 8419, 8423, 8429, 8431, 8443, 8447, 8461, 8467, 8501, 8513, 8521, 8527, 8537, 8539, 8543, 8563, 8573, 8581, 8597, 8599, 8609, 8623, 8627, 8629, 8641, 8647, 8663, 8669, 8677, 8681, 8689, 8693, 8699, 8707, 8713, 8719, 8731, 8737, 8741, 8747, 8753, 8761, 8779, 8783, 8803, 8807, 8819, 8821, 8831, 8837, 8839, 8849, 8861, 8863, 8867, 8887, 8893, 8923, 8929, 8933, 8941, 8951, 8963, 8969, 8971, 8999, 9001, 9007, 9011, 9013, 9029, 9041, 9043, 9049, 9059, 9067, 9091, 9103, 9109, 9127, 9133, 9137, 9151, 9157, 9161, 9173, 9181, 9187, 9199, 9203, 9209, 9221, 9227, 9239, 9241, 9257, 9277, 9281, 9283, 9293, 9311, 9319, 9323, 9337, 9341, 9343, 9349, 9371, 9377, 9391, 9397, 9403, 9413, 9419, 9421, 9431, 9433, 9437, 9439, 9461, 9463, 9467, 9473, 9479, 9491, 9497, 9511, 9521, 9533, 9539, 9547, 9551, 9587, 9601, 9613, 9619, 9623, 9629, 9631, 9643, 9649, 9661, 9677, 9679, 9689, 9697, 9719, 9721, 9733, 9739, 9743, 9749, 9767, 9769, 9781, 9787, 9791, 9803, 9811, 9817, 9829, 9833, 9839, 9851, 9857, 9859, 9871, 9883, 9887, 9901, 9907, 9923, 9929, 9931, 9941, 9949, 9967, 9973], @cache_up_to=30, @mod_candidates=[1, 7, 11, 13, 17, 19, 23, 29]>"
  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"
  25    ]
  26   },
  27   {
  28    "cell_type": "code",
  29    "execution_count": 2,
  30    "metadata": {
  31     "collapsed": false
  32    },
  33    "outputs": [
  34     {
  35      "data": {
  36       "text/plain": [
  37        ":to_r"
  38       ]
  39      },
  40      "execution_count": 2,
  41      "metadata": {},
  42      "output_type": "execute_result"
  43     }
  44    ],
  45    "source": [
  46     "class Array\n",
  47     "  def to_i\n",
  48     "    self.map {|d| d.to_s}.join.to_i\n",
  49     "  end\n",
  50     "  \n",
  51     "  def to_r\n",
  52     "    Rational(self[0].to_i, self[1].to_i)\n",
  53     "  end\n",
  54     "end"
  55    ]
  56   },
  57   {
  58    "cell_type": "code",
  59    "execution_count": 3,
  60    "metadata": {
  61     "collapsed": false
  62    },
  63    "outputs": [
  64     {
  65      "data": {
  66       "text/plain": [
  67        ":to_digits"
  68       ]
  69      },
  70      "execution_count": 3,
  71      "metadata": {},
  72      "output_type": "execute_result"
  73     }
  74    ],
  75    "source": [
  76     "class Integer\n",
  77     "  def to_digits\n",
  78     "    self.to_s.split('').map {|d| d.to_i}\n",
  79     "  end\n",
  80     "end "
  81    ]
  82   },
  83   {
  84    "cell_type": "code",
  85    "execution_count": 4,
  86    "metadata": {
  87     "collapsed": false
  88    },
  89    "outputs": [
  90     {
  91      "data": {
  92       "text/plain": [
  93        ":all_rotations"
  94       ]
  95      },
  96      "execution_count": 4,
  97      "metadata": {},
  98      "output_type": "execute_result"
  99     }
 100    ],
 101    "source": [
 102     "class Array\n",
 103     "  def all_rotations\n",
 104     "    (0...self.length).map {|r| self.rotate(r)}\n",
 105     "  end\n",
 106     "end"
 107    ]
 108   },
 109   {
 110    "cell_type": "code",
 111    "execution_count": 5,
 112    "metadata": {
 113     "collapsed": false
 114    },
 115    "outputs": [
 116     {
 117      "data": {
 118       "text/plain": [
 119        "[[1, 2, 3], [2, 3, 1], [3, 1, 2]]"
 120       ]
 121      },
 122      "execution_count": 5,
 123      "metadata": {},
 124      "output_type": "execute_result"
 125     }
 126    ],
 127    "source": [
 128     "[1,2,3].all_rotations"
 129    ]
 130   },
 131   {
 132    "cell_type": "code",
 133    "execution_count": 6,
 134    "metadata": {
 135     "collapsed": false
 136    },
 137    "outputs": [
 138     {
 139      "data": {
 140       "text/plain": [
 141        "[123, 231, 312]"
 142       ]
 143      },
 144      "execution_count": 6,
 145      "metadata": {},
 146      "output_type": "execute_result"
 147     }
 148    ],
 149    "source": [
 150     "[1,2,3].all_rotations.map {|n| n.to_i}"
 151    ]
 152   },
 153   {
 154    "cell_type": "code",
 155    "execution_count": 7,
 156    "metadata": {
 157     "collapsed": false
 158    },
 159    "outputs": [
 160     {
 161      "data": {
 162       "text/plain": [
 163        "[false, false, false]"
 164       ]
 165      },
 166      "execution_count": 7,
 167      "metadata": {},
 168      "output_type": "execute_result"
 169     }
 170    ],
 171    "source": [
 172     "[1,2,3].all_rotations.map {|n| n.to_i}.map {|n| $primes.include? n}"
 173    ]
 174   },
 175   {
 176    "cell_type": "code",
 177    "execution_count": 8,
 178    "metadata": {
 179     "collapsed": false
 180    },
 181    "outputs": [
 182     {
 183      "data": {
 184       "text/plain": [
 185        "[true, true]"
 186       ]
 187      },
 188      "execution_count": 8,
 189      "metadata": {},
 190      "output_type": "execute_result"
 191     }
 192    ],
 193    "source": [
 194     "17.to_digits.all_rotations.map {|n| n.to_i}.map {|n| $primes.include? n}"
 195    ]
 196   },
 197   {
 198    "cell_type": "code",
 199    "execution_count": 9,
 200    "metadata": {
 201     "collapsed": false
 202    },
 203    "outputs": [
 204     {
 205      "data": {
 206       "text/plain": [
 207        "false"
 208       ]
 209      },
 210      "execution_count": 9,
 211      "metadata": {},
 212      "output_type": "execute_result"
 213     }
 214    ],
 215    "source": [
 216     "[1,2,3].all_rotations.map {|n| n.to_i}.all? {|n| $primes.include? n}"
 217    ]
 218   },
 219   {
 220    "cell_type": "code",
 221    "execution_count": 10,
 222    "metadata": {
 223     "collapsed": false
 224    },
 225    "outputs": [
 226     {
 227      "data": {
 228       "text/plain": [
 229        "true"
 230       ]
 231      },
 232      "execution_count": 10,
 233      "metadata": {},
 234      "output_type": "execute_result"
 235     }
 236    ],
 237    "source": [
 238     "17.to_digits.all_rotations.map {|n| n.to_i}.all? {|n| $primes.include? n}"
 239    ]
 240   },
 241   {
 242    "cell_type": "code",
 243    "execution_count": 11,
 244    "metadata": {
 245     "collapsed": false
 246    },
 247    "outputs": [
 248     {
 249      "data": {
 250       "text/plain": [
 251        ":circular_prime?"
 252       ]
 253      },
 254      "execution_count": 11,
 255      "metadata": {},
 256      "output_type": "execute_result"
 257     }
 258    ],
 259    "source": [
 260     "class Integer\n",
 261     "  @@primes = Primes.instance\n",
 262     "  \n",
 263     "  def prime?\n",
 264     "    @@primes.include? self\n",
 265     "  end\n",
 266     "  \n",
 267     "  def pl\n",
 268     "    @@primes.primes.length\n",
 269     "  end\n",
 270     "  \n",
 271     "  def circular_prime?\n",
 272     "    self.to_digits.all_rotations.map {|n| n.to_i}.all? {|n| @@primes.include? n} if self.prime?\n",
 273     "  end\n",
 274     "end"
 275    ]
 276   },
 277   {
 278    "cell_type": "code",
 279    "execution_count": 11,
 280    "metadata": {
 281     "collapsed": false
 282    },
 283    "outputs": [
 284     {
 285      "data": {
 286       "text/plain": [
 287        ":circular_prime?"
 288       ]
 289      },
 290      "execution_count": 11,
 291      "metadata": {},
 292      "output_type": "execute_result"
 293     }
 294    ],
 295    "source": [
 296     "class Integer\n",
 297     "  @@primes = Primes.instance\n",
 298     "  \n",
 299     "  def prime?\n",
 300     "    @@primes.include? self\n",
 301     "  end\n",
 302     "  \n",
 303     "  def pl\n",
 304     "    @@primes.primes.length\n",
 305     "  end\n",
 306     "  \n",
 307     "  def circular_prime?\n",
 308     "    self.to_digits.all_rotations.map {|n| n.to_i}.all? {|n| n.prime?} if self.prime?\n",
 309     "  end\n",
 310     "end"
 311    ]
 312   },
 313   {
 314    "cell_type": "code",
 315    "execution_count": 12,
 316    "metadata": {
 317     "collapsed": false
 318    },
 319    "outputs": [
 320     {
 321      "data": {
 322       "text/plain": [
 323        "1229"
 324       ]
 325      },
 326      "execution_count": 12,
 327      "metadata": {},
 328      "output_type": "execute_result"
 329     }
 330    ],
 331    "source": [
 332     "0.pl"
 333    ]
 334   },
 335   {
 336    "cell_type": "code",
 337    "execution_count": 13,
 338    "metadata": {
 339     "collapsed": false
 340    },
 341    "outputs": [
 342     {
 343      "data": {
 344       "text/plain": [
 345        "[2, 3, 5, 7, 11, 13, 17, 31, 37, 71, 73, 79, 97]"
 346       ]
 347      },
 348      "execution_count": 13,
 349      "metadata": {},
 350      "output_type": "execute_result"
 351     }
 352    ],
 353    "source": [
 354     "(2..100).select {|n| n.circular_prime?}"
 355    ]
 356   },
 357   {
 358    "cell_type": "code",
 359    "execution_count": 14,
 360    "metadata": {
 361     "collapsed": false
 362    },
 363    "outputs": [
 364     {
 365      "data": {
 366       "text/plain": [
 367        "[2, 3, 5, 7, 11, 13, 17, 31, 37, 71, 73, 79, 97]"
 368       ]
 369      },
 370      "execution_count": 14,
 371      "metadata": {},
 372      "output_type": "execute_result"
 373     }
 374    ],
 375    "source": [
 376     "(2..100).select {|n| n.circular_prime?}"
 377    ]
 378   },
 379   {
 380    "cell_type": "code",
 381    "execution_count": 15,
 382    "metadata": {
 383     "collapsed": false
 384    },
 385    "outputs": [
 386     {
 387      "data": {
 388       "text/plain": [
 389        "13"
 390       ]
 391      },
 392      "execution_count": 15,
 393      "metadata": {},
 394      "output_type": "execute_result"
 395     }
 396    ],
 397    "source": [
 398     "(2..100).select {|n| n.circular_prime?}.length"
 399    ]
 400   },
 401   {
 402    "cell_type": "code",
 403    "execution_count": 16,
 404    "metadata": {
 405     "collapsed": false
 406    },
 407    "outputs": [],
 408    "source": [
 409     "# ps = $primes.take_while {|i| i <= 10**6}\n",
 410     "# ps.length"
 411    ]
 412   },
 413   {
 414    "cell_type": "code",
 415    "execution_count": 17,
 416    "metadata": {
 417     "collapsed": false
 418    },
 419    "outputs": [],
 420    "source": [
 421     "# (2..10**4).select {|n| n.circular_prime?}"
 422    ]
 423   },
 424   {
 425    "cell_type": "code",
 426    "execution_count": 18,
 427    "metadata": {
 428     "collapsed": false
 429    },
 430    "outputs": [
 431     {
 432      "name": "stdout",
 433      "output_type": "stream",
 434      "text": [
 435       "Time elapsed 0.125950399 seconds, going from 1229 to 1230 primes cached\n"
 436      ]
 437     },
 438     {
 439      "data": {
 440       "text/plain": [
 441        "33"
 442       ]
 443      },
 444      "execution_count": 18,
 445      "metadata": {},
 446      "output_type": "execute_result"
 447     }
 448    ],
 449    "source": [
 450     "pl0 = 0.pl\n",
 451     "beginning_time = Time.now\n",
 452     "cps = (2..10**4).select {|n| n.circular_prime?}\n",
 453     "end_time = Time.now\n",
 454     "pl1 = 0.pl\n",
 455     "puts \"Time elapsed #{(end_time - beginning_time)} seconds, going from #{pl0} to #{pl1} primes cached\"\n",
 456     "cps.length"
 457    ]
 458   },
 459   {
 460    "cell_type": "code",
 461    "execution_count": 19,
 462    "metadata": {
 463     "collapsed": false
 464    },
 465    "outputs": [
 466     {
 467      "name": "stdout",
 468      "output_type": "stream",
 469      "text": [
 470       "Time elapsed 0.123380027 seconds, going from 1230 to 1230 primes cached\n"
 471      ]
 472     },
 473     {
 474      "data": {
 475       "text/plain": [
 476        "33"
 477       ]
 478      },
 479      "execution_count": 19,
 480      "metadata": {},
 481      "output_type": "execute_result"
 482     }
 483    ],
 484    "source": [
 485     "pl0 = 0.pl\n",
 486     "beginning_time = Time.now\n",
 487     "cps = (2..10**4).select {|n| n.circular_prime?}\n",
 488     "end_time = Time.now\n",
 489     "pl1 = 0.pl\n",
 490     "puts \"Time elapsed #{(end_time - beginning_time)} seconds, going from #{pl0} to #{pl1} primes cached\"\n",
 491     "cps.length"
 492    ]
 493   },
 494   {
 495    "cell_type": "code",
 496    "execution_count": 20,
 497    "metadata": {
 498     "collapsed": false
 499    },
 500    "outputs": [
 501     {
 502      "name": "stdout",
 503      "output_type": "stream",
 504      "text": [
 505       "Time elapsed 9.59874264 seconds, going from 1230 to 9593 primes cached\n"
 506      ]
 507     },
 508     {
 509      "data": {
 510       "text/plain": [
 511        "43"
 512       ]
 513      },
 514      "execution_count": 20,
 515      "metadata": {},
 516      "output_type": "execute_result"
 517     }
 518    ],
 519    "source": [
 520     "pl0 = 0.pl\n",
 521     "beginning_time = Time.now\n",
 522     "cps = (2..10**5).select {|n| n.circular_prime?}\n",
 523     "end_time = Time.now\n",
 524     "pl1 = 0.pl\n",
 525     "puts \"Time elapsed #{(end_time - beginning_time)} seconds, going from #{pl0} to #{pl1} primes cached\"\n",
 526     "cps.length"
 527    ]
 528   },
 529   {
 530    "cell_type": "code",
 531    "execution_count": 21,
 532    "metadata": {
 533     "collapsed": false
 534    },
 535    "outputs": [
 536     {
 537      "name": "stdout",
 538      "output_type": "stream",
 539      "text": [
 540       "Time elapsed 7.768858416 seconds, going from 9593 to 9593 primes cached\n"
 541      ]
 542     },
 543     {
 544      "data": {
 545       "text/plain": [
 546        "43"
 547       ]
 548      },
 549      "execution_count": 21,
 550      "metadata": {},
 551      "output_type": "execute_result"
 552     }
 553    ],
 554    "source": [
 555     "pl0 = 0.pl\n",
 556     "beginning_time = Time.now\n",
 557     "cps = (2..10**5).select {|n| n.circular_prime?}\n",
 558     "end_time = Time.now\n",
 559     "pl1 = 0.pl\n",
 560     "puts \"Time elapsed #{(end_time - beginning_time)} seconds, going from #{pl0} to #{pl1} primes cached\"\n",
 561     "cps.length"
 562    ]
 563   },
 564   {
 565    "cell_type": "code",
 566    "execution_count": 22,
 567    "metadata": {
 568     "collapsed": false
 569    },
 570    "outputs": [
 571     {
 572      "name": "stdout",
 573      "output_type": "stream",
 574      "text": [
 575       "Time elapsed 710.264030183 seconds, going from 9593 to 78499 primes cached\n"
 576      ]
 577     },
 578     {
 579      "data": {
 580       "text/plain": [
 581        "55"
 582       ]
 583      },
 584      "execution_count": 22,
 585      "metadata": {},
 586      "output_type": "execute_result"
 587     }
 588    ],
 589    "source": [
 590     "pl0 = 0.pl\n",
 591     "beginning_time = Time.now\n",
 592     "cps = (2..10**6).select {|n| n.circular_prime?}\n",
 593     "end_time = Time.now\n",
 594     "pl1 = 0.pl\n",
 595     "puts \"Time elapsed #{(end_time - beginning_time)} seconds, going from #{pl0} to #{pl1} primes cached\"\n",
 596     "cps.length"
 597    ]
 598   },
 599   {
 600    "cell_type": "code",
 601    "execution_count": 23,
 602    "metadata": {
 603     "collapsed": false
 604    },
 605    "outputs": [
 606     {
 607      "name": "stdout",
 608      "output_type": "stream",
 609      "text": [
 610       "Time elapsed 597.009405584 seconds, going from 78499 to 78499 primes cached\n"
 611      ]
 612     },
 613     {
 614      "data": {
 615       "text/plain": [
 616        "55"
 617       ]
 618      },
 619      "execution_count": 23,
 620      "metadata": {},
 621      "output_type": "execute_result"
 622     }
 623    ],
 624    "source": [
 625     "pl0 = 0.pl\n",
 626     "beginning_time = Time.now\n",
 627     "cps = (2..10**6).select {|n| n.circular_prime?}\n",
 628     "end_time = Time.now\n",
 629     "pl1 = 0.pl\n",
 630     "puts \"Time elapsed #{(end_time - beginning_time)} seconds, going from #{pl0} to #{pl1} primes cached\"\n",
 631     "cps.length"
 632    ]
 633   },
 634   {
 635    "cell_type": "code",
 636    "execution_count": null,
 637    "metadata": {
 638     "collapsed": true
 639    },
 640    "outputs": [],
 641    "source": []
 642   }
 643  ],
 644  "metadata": {
 645   "kernelspec": {
 646    "display_name": "Ruby 2.4.0",
 647    "language": "ruby",
 648    "name": "ruby"
 649   },
 650   "language_info": {
 651    "file_extension": ".rb",
 652    "mimetype": "application/x-ruby",
 653    "name": "ruby",
 654    "version": "2.4.0"
 655   }
 656  },
 657  "nbformat": 4,
 658  "nbformat_minor": 0
 659 }