151212(4)

Ruby


Hilbert prime(2)

もう少し調べてみた。

def A057948(n)
  # m以下のHilbert primeを探す
  m = 10 ** 6
  list = Array.new(m + 1, false)
  1.step(m, 4){|i| list[i] = true}
  i = 5
  while i * i <= m
    if list[i]
      j = i + i
      while j <= m
        list[j] = false
        j += i
      end
    end
    i += 1
  end
  (5..m).select{|i| list[i]}[0..n]
end

p A057948(10 ** 3)

出力結果
[5, 9, 13, 17, 21, 29, 33, 37, 41, 49, 53, 57, 61, 69, 73, 77, 89, 93, 97, 101, 109, 113, 121, 129, 133, 137, 141, 149, 157, 161, 173, 177, 181, 193, 197, 201, 209, 213, 217, 229, 233, 237, 241, 249, 253, 257, 269, 277, 281, 293, 301, 309, 313, 317, 321, 329, 337, 341, 349, 353, 361, 373, 381, 389, 393, 397, 401, 409, 413, 417, 421, 433, 437, 449, 453, 457, 461, 469, 473, 489, 497, 501, 509, 517, 521, 529, 537, 541, 553, 557, 569, 573, 577, 581, 589, 593, 597, 601, 613, 617, 633, 641, 649, 653, 661, 669, 673, 677, 681, 701, 709, 713, 717, 721, 733, 737, 749, 753, 757, 761, 769, 773, 781, 789, 797, 809, 813, 817, 821, 829, 849, 853, 857, 869, 877, 881, 889, 893, 913, 917, 921, 929, 933, 937, 941, 953, 961, 973, 977, 989, 993, 997, 1009, 1013, 1021, 1033, 1041, 1049, 1057, 1061, 1069, 1077, 1081, 1093, 1097, 1101, 1109, 1117, 1121, 1129, 1133, 1137, 1141, 1149, 1153, 1169, 1177, 1181, 1193, 1201, 1213, 1217, 1229, 1237, 1249, 1253, 1257, 1273, 1277, 1289, 1293, 1297, 1301, 1317, 1321, 1329, 1333, 1337, 1349, 1357, 1361, 1373, 1381, 1389, 1393, 1397, 1401, 1409, 1429, 1433, 1437, 1441, 1453, 1457, 1461, 1473, 1477, 1481, 1489, 1493, 1497, 1501, 1509, 1529, 1541, 1549, 1553, 1561, 1569, 1577, 1589, 1597, 1601, 1609, 1613, 1621, 1633, 1637, 1641, 1657, 1661, 1669, 1673, 1689, 1693, 1697, 1709, 1713, 1721, 1733, 1741, 1753, 1757, 1761, 1777, 1789, 1793, 1797, 1801, 1817, 1821, 1829, 1837, 1841, 1849, 1857, 1861, 1873, 1877, 1889, 1893, 1897, 1901, 1909, 1913, 1929, 1933, 1941, 1949, 1957, 1969, 1973, 1977, 1981, 1993, 1997, 2017, 2021, 2029, 2033, 2049, 2053, 2069, 2073, 2077, 2081, 2089, 2101, 2113, 2129, 2137, 2141, 2149, 2153, 2157, 2161, 2177, 2181, 2189, 2201, 2209, 2213, 2217, 2221, 2229, 2237, 2253, 2269, 2273, 2281, 2293, 2297, 2309, 2317, 2321, 2333, 2341, 2357, 2361, 2369, 2377, 2381, 2389, 2393, 2413, 2417, 2429, 2433, 2437, 2441, 2449, 2453, 2461, 2469, 2473, 2477, 2481, 2489, 2497, 2513, 2517, 2521, 2537, 2549, 2557, 2569, 2573, 2577, 2589, 2593, 2609, 2617, 2621, 2629, 2633, 2641, 2649, 2653, 2657, 2661, 2677, 2681, 2689, 2693, 2713, 2721, 2729, 2733, 2741, 2749, 2753, 2757, 2761, 2773, 2777, 2789, 2797, 2801, 2833, 2837, 2841, 2857, 2861, 2869, 2881, 2893, 2897, 2901, 2909, 2913, 2917, 2921, 2933, 2949, 2953, 2957, 2969, 2973, 2981, 3001, 3013, 3017, 3037, 3041, 3049, 3053, 3057, 3061, 3073, 3089, 3093, 3097, 3101, 3109, 3113, 3117, 3121, 3137, 3149, 3153, 3169, 3173, 3181, 3189, 3193, 3197, 3209, 3217, 3221, 3229, 3241, 3253, 3257, 3261, 3269, 3273, 3301, 3309, 3313, 3317, 3329, 3337, 3353, 3361, 3369, 3373, 3377, 3389, 3397, 3401, 3409, 3413, 3421, 3433, 3437, 3449, 3453, 3457, 3461, 3469, 3473, 3481, 3489, 3493, 3513, 3517, 3521, 3529, 3533, 3541, 3557, 3561, 3569, 3581, 3593, 3613, 3617, 3629, 3637, 3641, 3661, 3669, 3673, 3677, 3693, 3697, 3701, 3709, 3713, 3733, 3749, 3761, 3769, 3777, 3781, 3793, 3797, 3817, 3821, 3829, 3833, 3837, 3841, 3849, 3853, 3873, 3877, 3881, 3889, 3901, 3909, 3917, 3921, 3929, 3937, 3941, 3949, 3953, 3957, 3981, 3989, 3997, 4001, 4009, 4013, 4021, 4037, 4049, 4057, 4061, 4073, 4093, 4101, 4109, 4117, 4129, 4133, 4153, 4157, 4169, 4177, 4189, 4193, 4197, 4201, 4213, 4217, 4229, 4237, 4241, 4249, 4253, 4261, 4269, 4273, 4281, 4289, 4297, 4309, 4313, 4317, 4333, 4337, 4341, 4349, 4353, 4357, 4373, 4377, 4393, 4397, 4409, 4413, 4417, 4421, 4429, 4441, 4449, 4457, 4461, 4481, 4489, 4493, 4497, 4501, 4513, 4517, 4529, 4533, 4541, 4549, 4561, 4569, 4577, 4593, 4597, 4601, 4609, 4613, 4621, 4629, 4637, 4649, 4657, 4661, 4673, 4677, 4681, 4701, 4713, 4721, 4729, 4733, 4737, 4741, 4749, 4757, 4769, 4781, 4789, 4793, 4801, 4813, 4817, 4821, 4829, 4837, 4841, 4853, 4857, 4861, 4873, 4877, 4881, 4889, 4897, 4909, 4933, 4937, 4957, 4969, 4973, 4989, 4993, 4997, 5001, 5009, 5021, 5029, 5033, 5041, 5053, 5077, 5081, 5089, 5093, 5097, 5101, 5113, 5129, 5137, 5149, 5153, 5169, 5173, 5177, 5189, 5197, 5201, 5209, 5221, 5233, 5237, 5241, 5257, 5261, 5269, 5273, 5277, 5281, 5293, 5297, 5309, 5333, 5349, 5357, 5361, 5377, 5381, 5393, 5401, 5413, 5417, 5433, 5437, 5441, 5449, 5461, 5469, 5477, 5489, 5493, 5497, 5501, 5509, 5521, 5533, 5541, 5549, 5557, 5561, 5569, 5573, 5581, 5601, 5609, 5613, 5633, 5637, 5641, 5653, 5657, 5669, 5677, 5689, 5693, 5701, 5717, 5721, 5737, 5741, 5749, 5753, 5761, 5773, 5789, 5793, 5801, 5813, 5821, 5833, 5849, 5853, 5857, 5861, 5869, 5873, 5881, 5893, 5897, 5909, 5921, 5937, 5953, 5961, 5969, 5977, 5981, 5997, 6009, 6013, 6017, 6029, 6033, 6037, 6041, 6049, 6053, 6073, 6077, 6081, 6089, 6101, 6113, 6117, 6121, 6133, 6157, 6169, 6173, 6181, 6189, 6193, 6197, 6209, 6217, 6221, 6229, 6233, 6241, 6249, 6257, 6261, 6269, 6277, 6281, 6289, 6297, 6301, 6313, 6317, 6329, 6333, 6337, 6349, 6353, 6361, 6373, 6377, 6389, 6393, 6397, 6421, 6429, 6433, 6449, 6457, 6469, 6473, 6481, 6493, 6509, 6521, 6529, 6533, 6537, 6541, 6553, 6557, 6569, 6577, 6581, 6589, 6593, 6609, 6621, 6629, 6637, 6653, 6661, 6673, 6677, 6689, 6701, 6709, 6717, 6729, 6733, 6737, 6753, 6761, 6769, 6781, 6793, 6797, 6801, 6809, 6821, 6829, 6833, 6841, 6857, 6861, 6869, 6881, 6889, 6901, 6913, 6917, 6933, 6937, 6941, 6949, 6961, 6973, 6977, 6997, 7001, 7009, 7013, 7017, 7037, 7041, 7053, 7057, 7061, 7069, 7073, 7097, 7109, 7113, 7117, 7121, 7129, 7133, 7149, 7153, 7169, 7177, 7181, 7193, 7197, 7201, 7213, 7217, 7229, 7233, 7237, 7249, 7253, 7269, 7273, 7277, 7297, 7309, 7313, 7321, 7333, 7341, 7349, 7357, 7369, 7377, 7393, 7401, 7409, 7417, 7433, 7441, 7457, 7477, 7481, 7489, 7493, 7509, 7513, 7517, 7529, 7537, 7541, 7549, 7561, 7573, 7577, 7589, 7593, 7597, 7601, 7609, 7613, 7617, 7621, 7629, 7637, 7649, 7653, 7661, 7669, 7673, 7681, 7697, 7717, 7721, 7729, 7737, 7741, 7753, 7757, 7773, 7781, 7789, 7793, 7817, 7829, 7841, 7849, 7853, 7861, 7873, 7877, 7901, 7909, 7933, 7937, 7941, 7949, 7961, 7977, 7981, 7989, 7993]