euler27.ipynb

   1 {
   2  "cells": [
   3   {
   4    "cell_type": "code",
   5    "execution_count": 6,
   6    "metadata": {
   7     "collapsed": false
   8    },
   9    "outputs": [
  10     {
  11      "data": {
  12       "text/plain": [
  13        "true"
  14       ]
  15      },
  16      "execution_count": 6,
  17      "metadata": {},
  18      "output_type": "execute_result"
  19     }
  20    ],
  21    "source": [
  22     "require \"awesome_print\"\n",
  23     "load 'primes.rb'"
  24    ]
  25   },
  26   {
  27    "cell_type": "code",
  28    "execution_count": 8,
  29    "metadata": {
  30     "collapsed": false,
  31     "scrolled": true
  32    },
  33    "outputs": [
  34     {
  35      "data": {
  36       "text/plain": [
  37        "#<Primes:0x0055d434088d98 @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]>"
  38       ]
  39      },
  40      "execution_count": 8,
  41      "metadata": {},
  42      "output_type": "execute_result"
  43     }
  44    ],
  45    "source": [
  46     "primes = Primes.instance;"
  47    ]
  48   },
  49   {
  50    "cell_type": "code",
  51    "execution_count": 18,
  52    "metadata": {
  53     "collapsed": false
  54    },
  55    "outputs": [
  56     {
  57      "data": {
  58       "text/plain": [
  59        "false"
  60       ]
  61      },
  62      "execution_count": 18,
  63      "metadata": {},
  64      "output_type": "execute_result"
  65     }
  66    ],
  67    "source": [
  68     "primes.include? 10008"
  69    ]
  70   },
  71   {
  72    "cell_type": "code",
  73    "execution_count": 19,
  74    "metadata": {
  75     "collapsed": false,
  76     "scrolled": true
  77    },
  78    "outputs": [
  79     {
  80      "data": {
  81       "text/plain": [
  82        "[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, 10007, 10009]"
  83       ]
  84      },
  85      "execution_count": 19,
  86      "metadata": {},
  87      "output_type": "execute_result"
  88     }
  89    ],
  90    "source": [
  91     "primes.primes"
  92    ]
  93   },
  94   {
  95    "cell_type": "code",
  96    "execution_count": 3,
  97    "metadata": {
  98     "collapsed": false,
  99     "scrolled": true
 100    },
 101    "outputs": [
 102     {
 103      "name": "stdout",
 104      "output_type": "stream",
 105      "text": [
 106       "0: 41\n",
 107       "1: 43\n",
 108       "2: 47\n",
 109       "3: 53\n",
 110       "4: 61\n",
 111       "5: 71\n",
 112       "6: 83\n",
 113       "7: 97\n",
 114       "8: 113\n",
 115       "9: 131\n",
 116       "10: 151\n",
 117       "11: 173\n",
 118       "12: 197\n",
 119       "13: 223\n",
 120       "14: 251\n",
 121       "15: 281\n",
 122       "16: 313\n",
 123       "17: 347\n",
 124       "18: 383\n",
 125       "19: 421\n",
 126       "20: 461\n",
 127       "21: 503\n",
 128       "22: 547\n",
 129       "23: 593\n",
 130       "24: 641\n",
 131       "25: 691\n",
 132       "26: 743\n",
 133       "27: 797\n",
 134       "28: 853\n",
 135       "29: 911\n",
 136       "30: 971\n",
 137       "31: 1033\n",
 138       "32: 1097\n",
 139       "33: 1163\n",
 140       "34: 1231\n",
 141       "35: 1301\n",
 142       "36: 1373\n",
 143       "37: 1447\n",
 144       "38: 1523\n",
 145       "39: 1601\n",
 146       "40: 1681\n",
 147       "41: 1763\n"
 148      ]
 149     },
 150     {
 151      "data": {
 152       "text/plain": [
 153        "42"
 154       ]
 155      },
 156      "execution_count": 3,
 157      "metadata": {},
 158      "output_type": "execute_result"
 159     }
 160    ],
 161    "source": [
 162     "42.times do |i|\n",
 163     "  puts(\"#{i}: #{i**2 + i + 41}\")\n",
 164     "end"
 165    ]
 166   },
 167   {
 168    "cell_type": "code",
 169    "execution_count": 5,
 170    "metadata": {
 171     "collapsed": false,
 172     "scrolled": true
 173    },
 174    "outputs": [
 175     {
 176      "name": "stdout",
 177      "output_type": "stream",
 178      "text": [
 179       "0: 1601\n",
 180       "1: 1523\n",
 181       "2: 1447\n",
 182       "3: 1373\n",
 183       "4: 1301\n",
 184       "5: 1231\n",
 185       "6: 1163\n",
 186       "7: 1097\n",
 187       "8: 1033\n",
 188       "9: 971\n",
 189       "10: 911\n",
 190       "11: 853\n",
 191       "12: 797\n",
 192       "13: 743\n",
 193       "14: 691\n",
 194       "15: 641\n",
 195       "16: 593\n",
 196       "17: 547\n",
 197       "18: 503\n",
 198       "19: 461\n",
 199       "20: 421\n",
 200       "21: 383\n",
 201       "22: 347\n",
 202       "23: 313\n",
 203       "24: 281\n",
 204       "25: 251\n",
 205       "26: 223\n",
 206       "27: 197\n",
 207       "28: 173\n",
 208       "29: 151\n",
 209       "30: 131\n",
 210       "31: 113\n",
 211       "32: 97\n",
 212       "33: 83\n",
 213       "34: 71\n",
 214       "35: 61\n",
 215       "36: 53\n",
 216       "37: 47\n",
 217       "38: 43\n",
 218       "39: 41\n",
 219       "40: 41\n",
 220       "41: 43\n",
 221       "42: 47\n",
 222       "43: 53\n",
 223       "44: 61\n",
 224       "45: 71\n",
 225       "46: 83\n",
 226       "47: 97\n",
 227       "48: 113\n",
 228       "49: 131\n",
 229       "50: 151\n",
 230       "51: 173\n",
 231       "52: 197\n",
 232       "53: 223\n",
 233       "54: 251\n",
 234       "55: 281\n",
 235       "56: 313\n",
 236       "57: 347\n",
 237       "58: 383\n",
 238       "59: 421\n",
 239       "60: 461\n",
 240       "61: 503\n",
 241       "62: 547\n",
 242       "63: 593\n",
 243       "64: 641\n",
 244       "65: 691\n",
 245       "66: 743\n",
 246       "67: 797\n",
 247       "68: 853\n",
 248       "69: 911\n",
 249       "70: 971\n",
 250       "71: 1033\n",
 251       "72: 1097\n",
 252       "73: 1163\n",
 253       "74: 1231\n",
 254       "75: 1301\n",
 255       "76: 1373\n",
 256       "77: 1447\n",
 257       "78: 1523\n",
 258       "79: 1601\n",
 259       "80: 1681\n",
 260       "81: 1763\n"
 261      ]
 262     },
 263     {
 264      "data": {
 265       "text/plain": [
 266        "82"
 267       ]
 268      },
 269      "execution_count": 5,
 270      "metadata": {},
 271      "output_type": "execute_result"
 272     }
 273    ],
 274    "source": [
 275     "82.times do |i|\n",
 276     "  puts(\"#{i}: #{i**2 - 79* i + 1601}\")\n",
 277     "end"
 278    ]
 279   },
 280   {
 281    "cell_type": "code",
 282    "execution_count": 20,
 283    "metadata": {
 284     "collapsed": false
 285    },
 286    "outputs": [
 287     {
 288      "name": "stdout",
 289      "output_type": "stream",
 290      "text": [
 291       "-9\n",
 292       "-8\n",
 293       "-7\n",
 294       "-6\n",
 295       "-5\n",
 296       "-4\n",
 297       "-3\n",
 298       "-2\n",
 299       "-1\n",
 300       "0\n",
 301       "1\n",
 302       "2\n",
 303       "3\n",
 304       "4\n",
 305       "5\n",
 306       "6\n",
 307       "7\n",
 308       "8\n",
 309       "9\n"
 310      ]
 311     },
 312     {
 313      "data": {
 314       "text/plain": [
 315        "-9..9"
 316       ]
 317      },
 318      "execution_count": 20,
 319      "metadata": {},
 320      "output_type": "execute_result"
 321     }
 322    ],
 323    "source": [
 324     "(-9..9).each {|i| puts(i)}"
 325    ]
 326   },
 327   {
 328    "cell_type": "code",
 329    "execution_count": 21,
 330    "metadata": {
 331     "collapsed": false
 332    },
 333    "outputs": [
 334     {
 335      "data": {
 336       "text/plain": [
 337        ":count_primes"
 338       ]
 339      },
 340      "execution_count": 21,
 341      "metadata": {},
 342      "output_type": "execute_result"
 343     }
 344    ],
 345    "source": [
 346     "def count_primes(primes, a, b)\n",
 347     "  n = 0\n",
 348     "  y = b\n",
 349     "  count = 0\n",
 350     "  while primes.include? y\n",
 351     "    count += 1\n",
 352     "    n += 1\n",
 353     "    y = n ** 2 + a * n + b\n",
 354     "  end\n",
 355     "  count  \n",
 356     "end"
 357    ]
 358   },
 359   {
 360    "cell_type": "code",
 361    "execution_count": 22,
 362    "metadata": {
 363     "collapsed": false
 364    },
 365    "outputs": [
 366     {
 367      "data": {
 368       "text/plain": [
 369        "40"
 370       ]
 371      },
 372      "execution_count": 22,
 373      "metadata": {},
 374      "output_type": "execute_result"
 375     }
 376    ],
 377    "source": [
 378     "count_primes(primes, 1, 41)"
 379    ]
 380   },
 381   {
 382    "cell_type": "code",
 383    "execution_count": 23,
 384    "metadata": {
 385     "collapsed": false
 386    },
 387    "outputs": [
 388     {
 389      "data": {
 390       "text/plain": [
 391        "80"
 392       ]
 393      },
 394      "execution_count": 23,
 395      "metadata": {},
 396      "output_type": "execute_result"
 397     }
 398    ],
 399    "source": [
 400     "count_primes(primes, -79, 1601)"
 401    ]
 402   },
 403   {
 404    "cell_type": "code",
 405    "execution_count": 33,
 406    "metadata": {
 407     "collapsed": false
 408    },
 409    "outputs": [
 410     {
 411      "data": {
 412       "text/plain": [
 413        "[[-50, 0], [-50, 1], [-50, 2], [-50, 3], [-50, 4], [-50, 5], [-50, 6], [-50, 7], [-50, 8], [-50, 9], [-50, 10], [-50, 11], [-50, 12], [-50, 13], [-50, 14], [-50, 15], [-50, 16], [-50, 17], [-50, 18], [-50, 19], [-50, 20], [-50, 21], [-50, 22], [-50, 23], [-50, 24], [-50, 25], [-50, 26], [-50, 27], [-50, 28], [-50, 29], [-50, 30], [-50, 31], [-50, 32], [-50, 33], [-50, 34], [-50, 35], [-50, 36], [-50, 37], [-50, 38], [-50, 39], [-50, 40], [-50, 41], [-50, 42], [-50, 43], [-50, 44], [-50, 45], [-50, 46], [-50, 47], [-50, 48], [-50, 49], [-50, 50], [-49, 0], [-49, 1], [-49, 2], [-49, 3], [-49, 4], [-49, 5], [-49, 6], [-49, 7], [-49, 8], [-49, 9], [-49, 10], [-49, 11], [-49, 12], [-49, 13], [-49, 14], [-49, 15], [-49, 16], [-49, 17], [-49, 18], [-49, 19], [-49, 20], [-49, 21], [-49, 22], [-49, 23], [-49, 24], [-49, 25], [-49, 26], [-49, 27], [-49, 28], [-49, 29], [-49, 30], [-49, 31], [-49, 32], [-49, 33], [-49, 34], [-49, 35], [-49, 36], [-49, 37], [-49, 38], [-49, 39], [-49, 40], [-49, 41], [-49, 42], [-49, 43], [-49, 44], [-49, 45], [-49, 46], [-49, 47], [-49, 48], [-49, 49], [-49, 50], [-48, 0], [-48, 1], [-48, 2], [-48, 3], [-48, 4], [-48, 5], [-48, 6], [-48, 7], [-48, 8], [-48, 9], [-48, 10], [-48, 11], [-48, 12], [-48, 13], [-48, 14], [-48, 15], [-48, 16], [-48, 17], [-48, 18], [-48, 19], [-48, 20], [-48, 21], [-48, 22], [-48, 23], [-48, 24], [-48, 25], [-48, 26], [-48, 27], [-48, 28], [-48, 29], [-48, 30], [-48, 31], [-48, 32], [-48, 33], [-48, 34], [-48, 35], [-48, 36], [-48, 37], [-48, 38], [-48, 39], [-48, 40], [-48, 41], [-48, 42], [-48, 43], [-48, 44], [-48, 45], [-48, 46], [-48, 47], [-48, 48], [-48, 49], [-48, 50], [-47, 0], [-47, 1], [-47, 2], [-47, 3], [-47, 4], [-47, 5], [-47, 6], [-47, 7], [-47, 8], [-47, 9], [-47, 10], [-47, 11], [-47, 12], [-47, 13], [-47, 14], [-47, 15], [-47, 16], [-47, 17], [-47, 18], [-47, 19], [-47, 20], [-47, 21], [-47, 22], [-47, 23], [-47, 24], [-47, 25], [-47, 26], [-47, 27], [-47, 28], [-47, 29], [-47, 30], [-47, 31], [-47, 32], [-47, 33], [-47, 34], [-47, 35], [-47, 36], [-47, 37], [-47, 38], [-47, 39], [-47, 40], [-47, 41], [-47, 42], [-47, 43], [-47, 44], [-47, 45], [-47, 46], [-47, 47], [-47, 48], [-47, 49], [-47, 50], [-46, 0], [-46, 1], [-46, 2], [-46, 3], [-46, 4], [-46, 5], [-46, 6], [-46, 7], [-46, 8], [-46, 9], [-46, 10], [-46, 11], [-46, 12], [-46, 13], [-46, 14], [-46, 15], [-46, 16], [-46, 17], [-46, 18], [-46, 19], [-46, 20], [-46, 21], [-46, 22], [-46, 23], [-46, 24], [-46, 25], [-46, 26], [-46, 27], [-46, 28], [-46, 29], [-46, 30], [-46, 31], [-46, 32], [-46, 33], [-46, 34], [-46, 35], [-46, 36], [-46, 37], [-46, 38], [-46, 39], [-46, 40], [-46, 41], [-46, 42], [-46, 43], [-46, 44], [-46, 45], [-46, 46], [-46, 47], [-46, 48], [-46, 49], [-46, 50], [-45, 0], [-45, 1], [-45, 2], [-45, 3], [-45, 4], [-45, 5], [-45, 6], [-45, 7], [-45, 8], [-45, 9], [-45, 10], [-45, 11], [-45, 12], [-45, 13], [-45, 14], [-45, 15], [-45, 16], [-45, 17], [-45, 18], [-45, 19], [-45, 20], [-45, 21], [-45, 22], [-45, 23], [-45, 24], [-45, 25], [-45, 26], [-45, 27], [-45, 28], [-45, 29], [-45, 30], [-45, 31], [-45, 32], [-45, 33], [-45, 34], [-45, 35], [-45, 36], [-45, 37], [-45, 38], [-45, 39], [-45, 40], [-45, 41], [-45, 42], [-45, 43], [-45, 44], [-45, 45], [-45, 46], [-45, 47], [-45, 48], [-45, 49], [-45, 50], [-44, 0], [-44, 1], [-44, 2], [-44, 3], [-44, 4], [-44, 5], [-44, 6], [-44, 7], [-44, 8], [-44, 9], [-44, 10], [-44, 11], [-44, 12], [-44, 13], [-44, 14], [-44, 15], [-44, 16], [-44, 17], [-44, 18], [-44, 19], [-44, 20], [-44, 21], [-44, 22], [-44, 23], [-44, 24], [-44, 25], [-44, 26], [-44, 27], [-44, 28], [-44, 29], [-44, 30], [-44, 31], [-44, 32], [-44, 33], [-44, 34], [-44, 35], [-44, 36], [-44, 37], [-44, 38], [-44, 39], [-44, 40], [-44, 41], [-44, 42], [-44, 43], [-44, 44], [-44, 45], [-44, 46], [-44, 47], [-44, 48], [-44, 49], [-44, 50], [-43, 0], [-43, 1], [-43, 2], [-43, 3], [-43, 4], [-43, 5], [-43, 6], [-43, 7], [-43, 8], [-43, 9], [-43, 10], [-43, 11], [-43, 12], [-43, 13], [-43, 14], [-43, 15], [-43, 16], [-43, 17], [-43, 18], [-43, 19], [-43, 20], [-43, 21], [-43, 22], [-43, 23], [-43, 24], [-43, 25], [-43, 26], [-43, 27], [-43, 28], [-43, 29], [-43, 30], [-43, 31], [-43, 32], [-43, 33], [-43, 34], [-43, 35], [-43, 36], [-43, 37], [-43, 38], [-43, 39], [-43, 40], [-43, 41], [-43, 42], [-43, 43], [-43, 44], [-43, 45], [-43, 46], [-43, 47], [-43, 48], [-43, 49], [-43, 50], [-42, 0], [-42, 1], [-42, 2], [-42, 3], [-42, 4], [-42, 5], [-42, 6], [-42, 7], [-42, 8], [-42, 9], [-42, 10], [-42, 11], [-42, 12], [-42, 13], [-42, 14], [-42, 15], [-42, 16], [-42, 17], [-42, 18], [-42, 19], [-42, 20], [-42, 21], [-42, 22], [-42, 23], [-42, 24], [-42, 25], [-42, 26], [-42, 27], [-42, 28], [-42, 29], [-42, 30], [-42, 31], [-42, 32], [-42, 33], [-42, 34], [-42, 35], [-42, 36], [-42, 37], [-42, 38], [-42, 39], [-42, 40], [-42, 41], [-42, 42], [-42, 43], [-42, 44], [-42, 45], [-42, 46], [-42, 47], [-42, 48], [-42, 49], [-42, 50], [-41, 0], [-41, 1], [-41, 2], [-41, 3], [-41, 4], [-41, 5], [-41, 6], [-41, 7], [-41, 8], [-41, 9], [-41, 10], [-41, 11], [-41, 12], [-41, 13], [-41, 14], [-41, 15], [-41, 16], [-41, 17], [-41, 18], [-41, 19], [-41, 20], [-41, 21], [-41, 22], [-41, 23], [-41, 24], [-41, 25], [-41, 26], [-41, 27], [-41, 28], [-41, 29], [-41, 30], [-41, 31], [-41, 32], [-41, 33], [-41, 34], [-41, 35], [-41, 36], [-41, 37], [-41, 38], [-41, 39], [-41, 40], [-41, 41], [-41, 42], [-41, 43], [-41, 44], [-41, 45], [-41, 46], [-41, 47], [-41, 48], [-41, 49], [-41, 50], [-40, 0], [-40, 1], [-40, 2], [-40, 3], [-40, 4], [-40, 5], [-40, 6], [-40, 7], [-40, 8], [-40, 9], [-40, 10], [-40, 11], [-40, 12], [-40, 13], [-40, 14], [-40, 15], [-40, 16], [-40, 17], [-40, 18], [-40, 19], [-40, 20], [-40, 21], [-40, 22], [-40, 23], [-40, 24], [-40, 25], [-40, 26], [-40, 27], [-40, 28], [-40, 29], [-40, 30], [-40, 31], [-40, 32], [-40, 33], [-40, 34], [-40, 35], [-40, 36], [-40, 37], [-40, 38], [-40, 39], [-40, 40], [-40, 41], [-40, 42], [-40, 43], [-40, 44], [-40, 45], [-40, 46], [-40, 47], [-40, 48], [-40, 49], [-40, 50], [-39, 0], [-39, 1], [-39, 2], [-39, 3], [-39, 4], [-39, 5], [-39, 6], [-39, 7], [-39, 8], [-39, 9], [-39, 10], [-39, 11], [-39, 12], [-39, 13], [-39, 14], [-39, 15], [-39, 16], [-39, 17], [-39, 18], [-39, 19], [-39, 20], [-39, 21], [-39, 22], [-39, 23], [-39, 24], [-39, 25], [-39, 26], [-39, 27], [-39, 28], [-39, 29], [-39, 30], [-39, 31], [-39, 32], [-39, 33], [-39, 34], [-39, 35], [-39, 36], [-39, 37], [-39, 38], [-39, 39], [-39, 40], [-39, 41], [-39, 42], [-39, 43], [-39, 44], [-39, 45], [-39, 46], [-39, 47], [-39, 48], [-39, 49], [-39, 50], [-38, 0], [-38, 1], [-38, 2], [-38, 3], [-38, 4], [-38, 5], [-38, 6], [-38, 7], [-38, 8], [-38, 9], [-38, 10], [-38, 11], [-38, 12], [-38, 13], [-38, 14], [-38, 15], [-38, 16], [-38, 17], [-38, 18], [-38, 19], [-38, 20], [-38, 21], [-38, 22], [-38, 23], [-38, 24], [-38, 25], [-38, 26], [-38, 27], [-38, 28], [-38, 29], [-38, 30], [-38, 31], [-38, 32], [-38, 33], [-38, 34], [-38, 35], [-38, 36], [-38, 37], [-38, 38], [-38, 39], [-38, 40], [-38, 41], [-38, 42], [-38, 43], [-38, 44], [-38, 45], [-38, 46], [-38, 47], [-38, 48], [-38, 49], [-38, 50], [-37, 0], [-37, 1], [-37, 2], [-37, 3], [-37, 4], [-37, 5], [-37, 6], [-37, 7], [-37, 8], [-37, 9], [-37, 10], [-37, 11], [-37, 12], [-37, 13], [-37, 14], [-37, 15], [-37, 16], [-37, 17], [-37, 18], [-37, 19], [-37, 20], [-37, 21], [-37, 22], [-37, 23], [-37, 24], [-37, 25], [-37, 26], [-37, 27], [-37, 28], [-37, 29], [-37, 30], [-37, 31], [-37, 32], [-37, 33], [-37, 34], [-37, 35], [-37, 36], [-37, 37], [-37, 38], [-37, 39], [-37, 40], [-37, 41], [-37, 42], [-37, 43], [-37, 44], [-37, 45], [-37, 46], [-37, 47], [-37, 48], [-37, 49], [-37, 50], [-36, 0], [-36, 1], [-36, 2], [-36, 3], [-36, 4], [-36, 5], [-36, 6], [-36, 7], [-36, 8], [-36, 9], [-36, 10], [-36, 11], [-36, 12], [-36, 13], [-36, 14], [-36, 15], [-36, 16], [-36, 17], [-36, 18], [-36, 19], [-36, 20], [-36, 21], [-36, 22], [-36, 23], [-36, 24], [-36, 25], [-36, 26], [-36, 27], [-36, 28], [-36, 29], [-36, 30], [-36, 31], [-36, 32], [-36, 33], [-36, 34], [-36, 35], [-36, 36], [-36, 37], [-36, 38], [-36, 39], [-36, 40], [-36, 41], [-36, 42], [-36, 43], [-36, 44], [-36, 45], [-36, 46], [-36, 47], [-36, 48], [-36, 49], [-36, 50], [-35, 0], [-35, 1], [-35, 2], [-35, 3], [-35, 4], [-35, 5], [-35, 6], [-35, 7], [-35, 8], [-35, 9], [-35, 10], [-35, 11], [-35, 12], [-35, 13], [-35, 14], [-35, 15], [-35, 16], [-35, 17], [-35, 18], [-35, 19], [-35, 20], [-35, 21], [-35, 22], [-35, 23], [-35, 24], [-35, 25], [-35, 26], [-35, 27], [-35, 28], [-35, 29], [-35, 30], [-35, 31], [-35, 32], [-35, 33], [-35, 34], [-35, 35], [-35, 36], [-35, 37], [-35, 38], [-35, 39], [-35, 40], [-35, 41], [-35, 42], [-35, 43], [-35, 44], [-35, 45], [-35, 46], [-35, 47], [-35, 48], [-35, 49], [-35, 50], [-34, 0], [-34, 1], [-34, 2], [-34, 3], [-34, 4], [-34, 5], [-34, 6], [-34, 7], [-34, 8], [-34, 9], [-34, 10], [-34, 11], [-34, 12], [-34, 13], [-34, 14], 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 414       ]
 415      },
 416      "execution_count": 33,
 417      "metadata": {},
 418      "output_type": "execute_result"
 419     }
 420    ],
 421    "source": [
 422     "coeffs = (-50..50).to_a.product((0..50).to_a);"
 423    ]
 424   },
 425   {
 426    "cell_type": "code",
 427    "execution_count": 34,
 428    "metadata": {
 429     "collapsed": false
 430    },
 431    "outputs": [
 432     {
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0, 1, 0, 0, 0, 4, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 2, 0, 1, 0, 1, 0, 0, 0, 6, 0, 1, 0, 0, 0, 2, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 3, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 3, 0, 0, 0, 0, 0, 2, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0]"
 436       ]
 437      },
 438      "execution_count": 34,
 439      "metadata": {},
 440      "output_type": "execute_result"
 441     }
 442    ],
 443    "source": [
 444     "coeffs.map {|a, b| count_primes(primes, a, b)}"
 445    ]
 446   },
 447   {
 448    "cell_type": "code",
 449    "execution_count": 35,
 450    "metadata": {
 451     "collapsed": false
 452    },
 453    "outputs": [
 454     {
 455      "data": {
 456       "text/plain": [
 457        "[-5, 47]"
 458       ]
 459      },
 460      "execution_count": 35,
 461      "metadata": {},
 462      "output_type": "execute_result"
 463     }
 464    ],
 465    "source": [
 466     "coeffs.max_by {|a, b| count_primes(primes, a, b)}"
 467    ]
 468   },
 469   {
 470    "cell_type": "code",
 471    "execution_count": 36,
 472    "metadata": {
 473     "collapsed": false
 474    },
 475    "outputs": [
 476     {
 477      "data": {
 478       "text/plain": [
 479        "43"
 480       ]
 481      },
 482      "execution_count": 36,
 483      "metadata": {},
 484      "output_type": "execute_result"
 485     }
 486    ],
 487    "source": [
 488     "count_primes(primes, -5, 47)"
 489    ]
 490   },
 491   {
 492    "cell_type": "code",
 493    "execution_count": 37,
 494    "metadata": {
 495     "collapsed": false,
 496     "scrolled": true
 497    },
 498    "outputs": [
 499     {
 500      "name": "stdout",
 501      "output_type": "stream",
 502      "text": [
 503       "0: 47 true\n",
 504       "1: 43 true\n",
 505       "2: 41 true\n",
 506       "3: 41 true\n",
 507       "4: 43 true\n",
 508       "5: 47 true\n",
 509       "6: 53 true\n",
 510       "7: 61 true\n",
 511       "8: 71 true\n",
 512       "9: 83 true\n",
 513       "10: 97 true\n",
 514       "11: 113 true\n",
 515       "12: 131 true\n",
 516       "13: 151 true\n",
 517       "14: 173 true\n",
 518       "15: 197 true\n",
 519       "16: 223 true\n",
 520       "17: 251 true\n",
 521       "18: 281 true\n",
 522       "19: 313 true\n",
 523       "20: 347 true\n",
 524       "21: 383 true\n",
 525       "22: 421 true\n",
 526       "23: 461 true\n",
 527       "24: 503 true\n",
 528       "25: 547 true\n",
 529       "26: 593 true\n",
 530       "27: 641 true\n",
 531       "28: 691 true\n",
 532       "29: 743 true\n",
 533       "30: 797 true\n",
 534       "31: 853 true\n",
 535       "32: 911 true\n",
 536       "33: 971 true\n",
 537       "34: 1033 true\n",
 538       "35: 1097 true\n",
 539       "36: 1163 true\n",
 540       "37: 1231 true\n",
 541       "38: 1301 true\n",
 542       "39: 1373 true\n",
 543       "40: 1447 true\n",
 544       "41: 1523 true\n",
 545       "42: 1601 true\n",
 546       "43: 1681 false\n",
 547       "44: 1763 false\n"
 548      ]
 549     },
 550     {
 551      "data": {
 552       "text/plain": [
 553        "45"
 554       ]
 555      },
 556      "execution_count": 37,
 557      "metadata": {},
 558      "output_type": "execute_result"
 559     }
 560    ],
 561    "source": [
 562     "45.times do |i|\n",
 563     "  puts(\"#{i}: #{i**2 - 5 * i + 47} #{primes.include? i**2 - 5 * i + 47}\")\n",
 564     "end"
 565    ]
 566   },
 567   {
 568    "cell_type": "code",
 569    "execution_count": 39,
 570    "metadata": {
 571     "collapsed": false
 572    },
 573    "outputs": [
 574     {
 575      "name": "stdout",
 576      "output_type": "stream",
 577      "text": [
 578       "-61, 971 : -59231\n"
 579      ]
 580     }
 581    ],
 582    "source": [
 583     "coeffs = (-999..999).to_a.product((0..1000).to_a)\n",
 584     "am, bm = coeffs.max_by {|a, b| count_primes(primes, a, b)}\n",
 585     "puts \"#{am}, #{bm} : #{am * bm}\""
 586    ]
 587   },
 588   {
 589    "cell_type": "code",
 590    "execution_count": null,
 591    "metadata": {
 592     "collapsed": true
 593    },
 594    "outputs": [],
 595    "source": []
 596   }
 597  ],
 598  "metadata": {
 599   "kernelspec": {
 600    "display_name": "Ruby 2.4.0",
 601    "language": "ruby",
 602    "name": "ruby"
 603   },
 604   "language_info": {
 605    "file_extension": ".rb",
 606    "mimetype": "application/x-ruby",
 607    "name": "ruby",
 608    "version": "2.4.0"
 609   }
 610  },
 611  "nbformat": 4,
 612  "nbformat_minor": 0
 613 }