MWSPrimes.m

//here we store the pre-computed mws_primes with respect to aux_int = 1 (MWSPrimes), aux_int = 2 (MWSPrimes2), aux_int = 4 (MWSPrimes4)
//we need a lower bound for mws_primes for the curve indexed by 115

LowerBound := [115];

// Mordell-Weil sieve primes computed with respect to the modulus 4*(p1*p2*p3)^4
 MWSPrimes4 := [
    [ 3, 5, 23, 31, 43, 61, 67, 107, 113, 173, 191, 193, 239, 283, 367, 431, 
    467, 491, 547, 569, 823, 971, 1069, 1283, 1489, 1553, 1597, 1777, 2243, 
    2927, 3517, 3607, 4261, 5039, 6067, 6287, 6659, 7151, 7649, 8317, 8539 ],
    [ 5, 7, 19, 23, 47, 79, 137, 139, 191, 347, 367, 607, 647, 701, 733, 881, 
    887, 1019, 1217, 1249, 1289, 1307, 1439, 1663, 1697, 1709, 1747, 1753, 1783,
    1979, 2099, 2591, 2711, 2957, 3373, 3583, 3803, 4001, 4409, 4621, 5449, 
    6047, 6343, 7057, 7369, 7577, 8081, 8117, 8171, 8423, 8831, 8863, 9277, 
    9677, 9859 ],
    [ 13, 41, 89, 107, 139, 179, 223, 397, 641, 673, 1361, 1489, 1663, 1759, 
    2437, 2749, 2803, 3499, 4817, 5381, 5737, 6451, 8719, 8803 ],
    [ 17, 19, 59, 163, 191, 311, 607, 823, 1117, 1451, 1873, 1973, 1979, 2309, 
    2857, 2897, 2971, 3167, 3631, 3637, 4261, 5039, 6217, 6287, 7151, 7541, 
    7951, 8317, 8539, 8753, 8893, 9187, 9431, 9733, 9859 ],
    [ 3, 7, 11, 19, 29, 31, 47, 59, 61, 73, 79, 83, 97, 101, 131, 137, 139, 157,
    173, 191, 199, 223, 293, 311, 317, 397, 421, 461, 467, 577, 607, 613, 643, 
    647, 683, 701, 733, 797, 919, 929, 983, 991, 1217, 1409, 1439, 1481, 1579, 
    1597, 1619, 1663, 1669, 1697, 1709, 1723, 1823, 1979, 1997, 2053, 2063, 
    2251, 2273, 2347, 2351, 2371, 2377, 2503, 2609, 2713, 2749, 2789, 2957, 
    3041, 3049, 3181, 3373, 3511, 3643, 3803, 4001, 4049, 4057, 4139, 4259, 
    4337, 4441, 4519, 4621, 4657, 4663, 4973, 5153, 5167, 5237, 5297, 5449, 
    5471, 5479, 5683, 5953, 6091, 6203, 6247, 6359, 6367, 6473, 6551, 6563, 
    6661, 7039, 7057, 7577, 7639, 7873, 8609, 9011, 9059, 9277, 9413, 9631 ],
    [ 3, 5, 17, 19, 29, 37, 47, 53, 83, 97, 157, 167, 179, 257, 263, 269, 271, 
    317, 409, 443, 461, 487, 491, 587, 593, 613, 619, 643, 647, 691, 727, 811, 
    983, 1013, 1097, 1117, 1237, 1289, 1433, 1451, 1453, 1499, 1601, 1607, 1721,
    1811, 1907, 1997, 2141, 2161, 2213, 2221, 2269, 2383, 2459, 2549, 2683, 
    2711, 2713, 2729, 2789, 2791, 2939, 2969, 3023, 3049, 3083, 3319, 3329, 
    3467, 3491, 3499, 3643, 3691, 3701, 3847, 3929, 4231, 4259, 4457, 4547, 
    4591, 4657, 4663, 4673, 4723, 4789, 5039, 5333, 5639, 5839, 6029, 6143, 
    6449, 6709, 6719, 6827, 7057, 7177, 7417, 7517, 7727, 7873, 7901, 8011, 
    8311, 8641, 8893, 8929, 9127, 9161, 9257, 9413 ],
    [ 191, 223, 317, 347, 359, 443, 557, 887, 1453, 1697, 2129, 2341, 2729, 
    2833, 3037, 3217, 3643, 4177, 5639, 6607, 6959, 9209, 9419 ],
    [ 191, 223, 317, 347, 359, 443, 557, 887, 1453, 1697, 2129, 2341, 2729, 
    2833, 3037, 3217, 3643, 4177, 5639, 6607, 6959, 9209, 9419 ],
    [ 3, 7, 11, 17, 23, 29, 31, 37, 41, 47, 59, 61, 67, 71, 73, 79, 83, 89, 101,
    107, 131, 137, 139, 149, 151, 163, 167, 179, 181, 191, 193, 199, 211, 223, 
    229, 233, 257, 269, 281, 311, 313, 317, 353, 367, 397, 401, 409, 439, 457, 
    479, 487, 499, 577, 607, 617, 641, 643, 653, 659, 661, 683, 701, 743, 751, 
    757, 769, 773, 797, 857, 919, 929, 937, 941, 947, 991, 1021, 1031, 1049, 
    1069, 1163, 1193, 1249, 1289, 1319, 1381, 1423, 1429, 1439, 1553, 1609, 
    1667, 1699, 1723, 1759, 1783, 1867, 1907, 1951, 1999, 2063, 2069, 2129, 
    2239, 2243, 2267, 2297, 2339, 2347, 2371, 2393, 2531, 2551, 2693, 2789, 
    2909, 2957, 3001, 3041, 3217, 3221, 3299, 3371, 3457, 3511, 3533, 3637, 
    3691, 3697, 3709, 3833, 3851, 3853, 3929, 3967, 4229, 4349, 4391, 4549, 
    4621, 4651, 4759, 4831, 4967, 5039, 5051, 5107, 5113, 5227, 5399, 5477, 
    5479, 5501, 5527, 5639, 5651, 5717, 5737, 5779, 5783, 5879, 5927, 5953, 
    6079, 6151, 6197, 6211, 6337, 6379, 6451, 6491, 6709, 6761, 6899, 6977, 
    7013, 7159, 7207, 7213, 7349, 7477, 7537, 7541, 7669, 7687, 7699, 7753, 
    7793, 7879, 7907, 7927, 8081, 8237, 8243, 8263, 8269, 8389, 8629, 8677, 
    8821, 8971, 9029, 9049, 9221, 9257, 9533, 9871 ],
    [ 11, 23, 101, 113, 173, 179, 181, 197, 251, 271, 487, 571, 619, 733, 887, 
    967, 1009, 1019, 1187, 1499, 1543, 1579, 1801, 2111, 2143, 2521, 2857, 3167,
    3329, 3797, 3863, 4657, 5749, 5897, 5927, 6599, 6793, 6949, 6961, 7649, 
    7703, 8263, 8929, 9337 ],
    [ 19, 47, 79, 191, 557, 647, 769, 1129, 1217, 1663, 1709, 2833, 3907, 4013, 
    4273, 4793, 5449, 5867, 6203, 7687, 8297, 9539, 9803 ],
    [ 11, 23, 53, 101, 113, 181, 197, 211, 227, 251, 499, 541, 569, 593, 619, 
    661, 941, 967, 1213, 1301, 1523, 1543, 1579, 2473, 2591, 2693, 2699, 2861, 
    3011, 3079, 3167, 3677, 3797, 3863, 4157, 4423, 4973, 5011, 5749, 5779, 
    6949, 7703, 8273, 8929, 9857 ],
    [ 7, 71, 109, 233, 499, 617, 863, 907, 919, 1013, 1439, 1571, 1609, 1999, 
    2399, 2953, 2999, 3037, 3323, 3919, 4337, 4481, 4937, 4967, 5519, 5531, 
    6053, 7907, 8171, 9377, 9521, 9901 ],
    [ 19, 61, 71, 191, 1873, 2141, 3163, 3167, 3433, 3517, 4157, 4423, 5279, 
    5437, 6067, 6883, 7283 ],
    [ 3, 5, 13, 17, 19, 43, 61, 107, 113, 191, 193, 359, 379, 383, 457, 521, 
    643, 947, 971, 1031, 1069, 1163, 1229, 1283, 1433, 1553, 1597, 1777, 1873, 
    2011, 2131, 2383, 2399, 2473, 2531, 2593, 2671, 2897, 2969, 3361, 4091, 
    4211, 4219, 4229, 4261, 5209, 5477, 5573, 5689, 6287, 6659, 6661, 6679, 
    6779, 6781, 6883, 7193, 7481, 8233, 8317, 8467, 8713, 9859, 9887 ],
    [ 13, 17, 31, 89, 101, 139, 167, 193, 223, 251, 271, 421, 487, 541, 677, 
    853, 1609, 1861, 2179, 2311, 2741, 4733, 6221, 6689, 6967, 8147, 9539, 9929 
    ],
    [ 17, 103, 107, 113, 191, 197, 239, 277, 311, 457, 541, 547, 557, 761, 863, 
    907, 937, 1553, 2161, 2243, 2269, 3931, 4159, 5419, 5791, 6131, 6619, 6781, 
    7187, 7283, 7499, 8101, 9931 ],
    [ 3, 5, 11, 31, 37, 41, 67, 73, 83, 109, 131, 137, 163, 167, 191, 193, 197, 
    199, 211, 223, 233, 271, 311, 313, 331, 401, 467, 499, 569, 593, 661, 691, 
    701, 719, 733, 743, 773, 809, 821, 839, 919, 937, 953, 967, 1031, 1039, 
    1051, 1109, 1373, 1399, 1459, 1499, 1663, 1699, 1709, 1831, 1847, 1867, 
    1901, 1907, 1913, 2089, 2129, 2153, 2341, 2351, 2741, 2843, 3083, 3089, 
    3163, 3229, 3307, 3323, 3413, 3461, 3541, 3769, 3823, 3931, 4073, 4253, 
    4357, 4391, 4457, 4463, 4597, 4621, 4651, 4751, 4861, 4931, 5147, 5563, 
    5903, 5939, 6029, 6361, 6653, 6779, 7151, 7229, 7309, 7451, 7507, 7621, 
    7993, 8123, 8429, 8467, 8623, 8629, 8837, 8887, 9323, 9689, 9901 ],
    [ 3, 11, 31, 37, 43, 61, 73, 83, 109, 139, 163, 167, 179, 181, 193, 223, 
    311, 313, 359, 499, 509, 569, 599, 613, 683, 719, 727, 733, 751, 1039, 1087,
    1187, 1231, 1567, 1667, 1699, 1709, 1823, 2341, 2357, 2609, 2633, 2729, 
    3319, 3541, 3659, 4421, 4691, 4751, 4889, 4919, 5273, 5297, 6029, 6317, 
    6547, 8263, 8623, 8839 ],
    [ 3, 7, 47, 101, 151, 163, 181, 233, 277, 401, 419, 461, 757, 929, 1019, 
    1087, 1213, 1229, 1439, 1621, 1693, 1889, 2731, 3067, 3253, 3259, 3373, 
    3517, 3571, 3617, 3853, 3919, 3943, 4021, 4027, 4093, 4457, 5507, 5669, 
    5869, 6661, 7333, 8269, 8363, 8369, 8819, 9199, 9901 ],
    [ 13, 23, 41, 43, 53, 79, 83, 101, 103, 157, 173, 181, 197, 227, 251, 337, 
    349, 541, 593, 599, 733, 967, 977, 1117, 1291, 1301, 1439, 1543, 1579, 1669,
    1693, 1801, 2153, 2857, 3319, 3329, 3797, 3851, 3863, 4093, 4133, 4597, 
    4931, 5749, 6037, 6211, 6337, 6427, 6949, 7649, 7703, 8263, 8353, 8929, 
    9151, 9323, 9371, 9769 ],
    [ 3, 7, 17, 19, 41, 83, 103, 107, 139, 151, 197, 239, 277, 337, 541, 547, 
    661, 683, 823, 1069, 1367, 1427, 1543, 1637, 1697, 1709, 1721, 1861, 1877, 
    1997, 1999, 2161, 2377, 2473, 2531, 2549, 2917, 2971, 3203, 3323, 3733, 
    3833, 3853, 3889, 4933, 5189, 5333, 5407, 5741, 5839, 5927, 5987, 6619, 
    6907, 6949, 7283, 7817, 8737 ],
    [ 19, 29, 43, 47, 53, 163, 167, 199, 281, 599, 719, 757, 811, 941, 1021, 
    1291, 1307, 1613, 1627, 1997, 2239, 2593, 2677, 2851, 2903, 3319, 4217, 
    5189, 5711, 5801, 5981 ],
    [ 3, 5, 13, 23, 41, 43, 47, 59, 67, 101, 103, 107, 127, 167, 193, 199, 229, 
    263, 269, 277, 281, 283, 293, 317, 337, 401, 421, 433, 467, 479, 487, 503, 
    547, 569, 599, 601, 613, 653, 677, 733, 739, 757, 883, 887, 907, 919, 1013, 
    1039, 1117, 1151, 1229, 1297, 1319, 1433, 1523, 1553, 1601, 1733, 1847, 
    1861, 1999, 2083, 2131, 2143, 2237, 2383, 2437, 2467, 2531, 2687, 2693, 
    2803, 2939, 2957, 3163, 3299, 3433, 3467, 3593, 3847, 3863, 3947, 4013, 
    4091, 4157, 4211, 4357, 4373, 4421, 4423, 4591, 4643, 4651, 4703, 4801, 
    4973, 5077, 5113, 5119, 5147, 5297, 5347, 5651, 5987, 6043, 6373, 6481, 
    6563, 6719, 6983, 7309, 7477, 7489, 8011, 8117, 8329, 8467, 8539, 8629, 
    8753, 8887, 9059, 9181, 9437, 9719, 9871 ],
    [ 5, 7, 13, 19, 41, 43, 53, 67, 71, 79, 89, 103, 113, 149, 191, 233, 239, 
    241, 257, 271, 487, 523, 617, 661, 673, 691, 739, 859, 883, 1039, 1051, 
    1069, 1193, 1217, 1481, 1621, 1933, 2029, 2113, 2269, 2371, 2707, 2797, 
    2843, 3011, 3163, 3319, 3413, 3617, 3769, 3779, 4091, 4157, 4337, 4409, 
    4783, 5197, 5449, 5507, 5531, 5563, 5711, 5897, 6067, 6073, 6269, 6673, 
    7639, 7901, 8233, 8467, 8719, 8849, 9181, 9199, 9431, 9433, 9437, 9631 ],
    [ 3, 5, 11, 17, 23, 31, 43, 71, 73, 79, 83, 97, 101, 103, 113, 127, 137, 
    167, 197, 199, 223, 251, 257, 281, 293, 311, 313, 337, 347, 349, 373, 389, 
    421, 443, 521, 547, 569, 577, 593, 599, 607, 617, 641, 647, 787, 809, 827, 
    829, 859, 883, 919, 929, 1019, 1061, 1153, 1193, 1201, 1471, 1483, 1493, 
    1511, 1567, 1657, 1753, 1801, 1823, 1831, 1933, 1951, 2017, 2083, 2129, 
    2137, 2143, 2161, 2203, 2287, 2377, 2393, 2423, 2437, 2543, 2551, 2591, 
    2647, 2657, 2663, 2777, 2819, 3049, 3167, 3187, 3301, 3329, 3463, 3529, 
    4201, 4229, 4273, 4817, 4993, 5233, 5441, 5807, 5897, 5903, 6311, 6551, 
    6553, 6673, 6689, 6703, 6719, 7109, 7121, 7193, 7211, 7561, 7577, 7591, 
    7883, 7919, 8017, 8081, 8117, 8171, 8297, 8431, 8521, 8609, 8647, 8699, 
    8821, 8951, 9029, 9103, 9151, 9791, 9829, 9907 ],
    [ 5, 7, 19, 23, 47, 79, 107, 139, 163, 313, 367, 443, 739, 823, 1193, 1237, 
    1249, 1481, 1543, 1663, 1697, 1753, 2099, 2203, 2711, 3041, 3301, 3373, 
    3643, 4231, 4723, 5119, 5167, 5449, 6199, 6203, 6803, 7057, 7477, 7549, 
    7577, 8461, 8821, 8863, 9227 ],
    [ 7, 17, 23, 37, 47, 67, 71, 89, 107, 167, 239, 241, 257, 491, 563, 613, 
    883, 1259, 1307, 1553, 1567, 1601, 1721, 2087, 2297, 2617, 2729, 2797, 2969,
    3253, 3391, 3529, 3833, 4013, 4703, 4789, 5231, 5333, 5407, 5591, 5867, 
    7039, 7451, 7727, 8573, 8669 ],
    [ 5, 7, 11, 19, 23, 67, 71, 89, 97, 107, 113, 139, 149, 167, 191, 211, 223, 
    229, 239, 311, 317, 349, 373, 379, 383, 467, 491, 541, 607, 631, 659, 661, 
    673, 709, 727, 757, 761, 797, 809, 983, 1013, 1021, 1051, 1069, 1091, 1109, 
    1117, 1187, 1193, 1213, 1223, 1237, 1307, 1451, 1523, 1627, 1663, 1759, 
    1783, 1811, 1901, 1997, 2017, 2089, 2113, 2131, 2179, 2239, 2309, 2341, 
    2389, 2441, 2459, 2477, 2591, 2621, 2687, 2689, 2693, 2819, 2851, 2857, 
    3221, 3257, 3559, 3833, 4051, 4133, 4201, 4219, 4357, 4493, 4597, 4783, 
    4817, 4943, 4951, 4967, 5273, 5279, 5381, 5449, 5479, 5717, 6029, 6073, 
    6229, 6277, 6301, 6481, 6521, 6883, 6977, 6997, 7577, 7699, 8087, 8329, 
    8353, 8419, 8443, 8699, 9551, 9749, 9811, 9833 ],
    [ 3, 7, 19, 47, 97, 101, 103, 151, 163, 233, 277, 283, 421, 461, 617, 811, 
    929, 983, 1087, 2087, 2459, 2549, 2767, 2797, 2851, 3253, 3373, 3919, 3943, 
    4021, 4153, 5531, 5557, 5669, 5981, 6101, 6661, 7013, 7109, 8269, 8369, 
    8971, 9619, 9901 ],
    [ 11, 43, 47, 59, 89, 103, 107, 113, 127, 229, 433, 503, 541, 571, 641, 761,
    769, 1033, 1129, 1153, 1289, 1291, 1321, 1451, 1601, 1823, 1861, 2281, 2441,
    2647, 2663, 2699, 2857, 3343, 3359, 3457, 3617, 3853, 5521, 5791, 6551, 
    6691, 6823, 7879, 8669, 9133, 9619, 9677, 9679 ],
    [ 23, 61, 67, 79, 101, 107, 151, 157, 173, 179, 181, 197, 211, 233, 271, 
    419, 421, 479, 487, 523, 593, 599, 619, 887, 941, 967, 1117, 1187, 1291, 
    1301, 1543, 1579, 2473, 2801, 2861, 2953, 3079, 3371, 3511, 3821, 3863, 
    4241, 4597, 4973, 5897, 6037, 6473, 6619, 6793, 6863, 6907, 7211, 7411, 
    7703, 8263, 9749, 9817 ],
    [ 11, 19, 23, 31, 41, 53, 179, 191, 283, 331, 449, 521, 593, 617, 661, 691, 
    907, 1019, 1307, 1663, 2297, 2671, 2719, 2797, 3203, 4127, 4447, 4657, 5381,
    5449, 5923, 6121, 6869, 8233, 8719, 8849, 9391, 9431 ],
    [ 3, 5, 7, 17, 19, 23, 31, 47, 59, 67, 71, 73, 97, 101, 131, 137, 139, 151, 
    173, 179, 181, 191, 211, 233, 239, 251, 277, 283, 313, 349, 401, 419, 433, 
    439, 443, 463, 487, 491, 503, 523, 593, 599, 607, 631, 677, 751, 769, 773, 
    857, 887, 947, 971, 1021, 1039, 1193, 1201, 1223, 1279, 1303, 1433, 1481, 
    1583, 1609, 1657, 1697, 1723, 1747, 1759, 1879, 1907, 1913, 1951, 2087, 
    2251, 2377, 2399, 2417, 2423, 2473, 2621, 2633, 3119, 3121, 3167, 3187, 
    3191, 3313, 3329, 3449, 3467, 3511, 3677, 3727, 3761, 3769, 3919, 4001, 
    4153, 4271, 4283, 4373, 4423, 4463, 4567, 4639, 4651, 4657, 4703, 4751, 
    4937, 4951, 4967, 5003, 5107, 5153, 5449, 5573, 5701, 5743, 5849, 5881, 
    5953, 5981, 6029, 6089, 6311, 6367, 6473, 6521, 6551, 6607, 6761, 6781, 
    6991, 6997, 7121, 7489, 7561, 7639, 8117, 8233, 8237, 8609, 8647, 8713, 
    8839, 8863, 9319, 9697 ],
    [ 7, 59, 107, 131, 139, 149, 179, 181, 227, 347, 383, 509, 541, 593, 647, 
    761, 821, 839, 853, 919, 1013, 1069, 1151, 1303, 2251, 2267, 2333, 2551, 
    2633, 2687, 2713, 2729, 2837, 2857, 3061, 3461, 3463, 3623, 3637, 3863, 
    4597, 4649, 4799, 5323, 5737, 5743, 6247, 6271, 6421, 6521, 7019, 8087, 
    8219, 8609, 8849 ],
    [ 3, 5, 11, 19, 43, 53, 79, 107, 109, 127, 193, 271, 277, 359, 503, 1021, 
    1213, 1229, 1319, 2063, 2153, 2347, 2551, 2617, 2903, 2971, 3319, 3461, 
    3691, 4019, 4253, 4493, 4561, 5021, 5233, 5807, 6287, 6451, 7517, 7699, 
    8369, 8863, 9013, 9811, 9871 ],
    [ 5, 11, 17, 19, 23, 31, 43, 47, 67, 97, 107, 113, 131, 149, 163, 197, 233, 
    239, 257, 283, 313, 367, 373, 431, 461, 487, 491, 593, 599, 701, 727, 769, 
    773, 787, 797, 811, 823, 857, 967, 1033, 1093, 1129, 1201, 1213, 1229, 1321,
    1549, 1697, 1747, 1783, 2111, 2273, 2459, 2521, 2707, 2909, 3313, 3449, 
    3467, 3469, 3557, 3559, 3911, 4051, 4967, 4969, 5413, 5717, 5827, 6151, 
    6173, 6359, 6473, 6661, 6673, 6823, 6991, 7489, 7561, 7583, 7649, 8179, 
    8243, 8641, 8863, 8963, 9227, 9551, 9719 ],
    [ 23, 41, 83, 101, 137, 157, 181, 197, 251, 293, 307, 349, 419, 479, 491, 
    499, 541, 571, 593, 599, 619, 709, 853, 967, 1151, 1201, 1301, 1373, 1439, 
    1543, 1579, 1693, 1879, 2087, 2239, 2309, 2399, 2609, 2699, 2741, 3323, 
    3329, 3499, 3863, 4003, 4129, 4157, 4597, 4799, 4801, 4909, 4951, 5081, 
    5381, 5431, 5507, 5527, 5647, 5807, 6949, 7349, 7607, 7759, 7873, 8263, 
    8719, 9221, 9349, 9497, 9769 ],
    [ 3, 5, 7, 13, 17, 19, 29, 47, 53, 59, 71, 83, 97, 103, 107, 109, 149, 163, 
    181, 191, 229, 251, 257, 269, 281, 311, 317, 331, 347, 353, 359, 383, 389, 
    397, 419, 431, 433, 457, 461, 479, 499, 577, 593, 599, 617, 647, 773, 809, 
    827, 863, 907, 911, 929, 947, 1021, 1109, 1213, 1229, 1237, 1249, 1321, 
    1367, 1409, 1433, 1439, 1453, 1571, 1613, 1619, 1721, 1753, 1787, 1949, 
    1997, 1999, 2003, 2161, 2377, 2399, 2579, 2591, 2621, 2731, 2749, 2777, 
    2797, 2927, 2953, 2969, 2999, 3049, 3271, 3323, 3371, 3449, 3469, 3491, 
    3529, 3541, 3659, 3727, 3853, 3943, 4013, 4079, 4093, 4129, 4337, 4481, 
    4567, 4657, 4673, 4723, 4751, 4789, 4871, 4877, 4933, 4937, 4943, 4967, 
    4987, 4999, 5261, 5413, 5417, 5507, 5519, 5531, 5641, 5669, 5749, 5849, 
    5857, 6053, 6287, 6301, 6337, 6473, 6599, 6791, 6899, 6947, 7013, 7127, 
    7177, 7297, 7331, 7351, 7451, 7499, 7517, 7577, 7583, 7589, 7829, 7877, 
    7907, 7951, 8017, 8053, 8171, 8363, 8369, 8423, 9157, 9277, 9377, 9431, 
    9521, 9539, 9791, 9817 ],
    [ 5, 13, 17, 19, 23, 31, 61, 107, 113, 167, 191, 193, 239, 367, 457, 521, 
    823, 971, 1069, 1229, 1433, 1553, 1597, 1627, 1777, 1873, 2207, 2251, 2473, 
    2593, 2897, 2927, 2963, 2969, 3361, 3623, 3931, 4051, 4229, 4261, 5209, 
    5431, 5443, 5477, 5573, 5689, 6067, 6661, 6781, 7027, 7151, 7159, 7187, 
    7193, 7481, 8233, 8317, 8539, 8623, 8713, 9551 ],
    [ 5, 19, 61, 67, 71, 113, 167, 173, 191, 193, 307, 359, 569, 971, 1069, 
    1163, 1327, 1489, 1553, 1597, 1777, 1787, 2087, 2179, 2243, 2251, 2531, 
    3359, 3517, 4261, 5039, 5431, 5927, 6659, 7151, 7649, 8317, 9643 ],
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    3469, 3581, 4201, 4937, 5281, 6269, 6653, 6871, 6949, 7283, 7457, 7823, 
    8737, 9203 ],
    [ 11, 19, 23, 53, 79, 251, 257, 313, 397, 593, 607, 613, 859, 967, 1453, 
    1459, 1489, 1721, 1747, 1811, 1823, 1987, 2239, 2377, 2521, 2609, 2663, 
    2689, 2707, 2917, 4649, 4931, 5081, 5701, 5821, 5851, 6151, 6221, 6323, 
    7027, 7103, 8009, 8243, 8783, 8849, 8867, 9157 ],
    [ 311, 359, 443, 467, 499, 541, 599, 709, 727, 911, 1021, 1117, 1163, 1307, 
    1523, 1663, 1777, 1993, 2017, 2053, 2459, 2687, 2689, 2777, 3319, 4271, 
    5023, 5297, 5449, 6977, 7043, 7639, 9551 ],
    [ 37, 41, 53, 67, 71, 131, 139, 197, 257, 313, 317, 563, 641, 643, 701, 
    1259, 1303, 1429, 1613, 1619, 1997, 2063, 2243, 2683, 2699, 2803, 2963, 
    3023, 4013, 4051, 4327, 4721, 6073, 6221, 6427, 7687, 9209 ],
    [ 5, 7, 17, 31, 37, 43, 47, 53, 59, 61, 97, 101, 109, 173, 181, 193, 223, 
    269, 379, 389, 401, 409, 491, 557, 647, 673, 683, 701, 757, 769, 863, 929, 
    977, 1061, 1283, 1321, 1373, 1381, 1567, 1627, 1693, 1721, 1801, 1997, 2011,
    2081, 2087, 2243, 2357, 2657, 2713, 2741, 2861, 3089, 3301, 3371, 3413, 
    3457, 3581, 3907, 3911, 4073, 4157, 4651, 4657, 4969, 5023, 5821, 5869, 
    6421, 6547, 6857, 7129, 7451, 7649, 8237, 8747, 9473, 9533, 9857 ],
    [ 11, 23, 41, 67, 101, 113, 137, 157, 173, 179, 197, 211, 241, 307, 541, 
    571, 593, 599, 619, 811, 853, 967, 971, 977, 1117, 1187, 1229, 1301, 1327, 
    1543, 2843, 3329, 3793, 3797, 3863, 4093, 4157, 4349, 4787, 4937, 6037, 
    6899, 6949, 7019, 7187, 7703, 7867, 8117, 8263, 8761, 9769 ],
    [ 3, 5, 7, 11, 17, 29, 31, 59, 67, 83, 97, 131, 137, 167, 179, 181, 193, 
    199, 223, 229, 233, 311, 313, 401, 443, 499, 569, 571, 593, 599, 631, 661, 
    683, 719, 733, 773, 821, 911, 953, 967, 971, 1039, 1087, 1109, 1459, 1699, 
    1709, 1747, 1823, 1847, 1901, 2027, 2039, 2069, 2083, 2153, 2309, 2437, 
    2609, 2687, 2713, 2741, 2843, 3019, 3089, 3119, 3229, 3319, 3541, 3581, 
    3593, 3623, 3631, 3833, 3881, 4001, 4013, 4019, 4073, 4157, 4253, 4283, 
    4421, 4463, 4751, 4793, 4919, 5077, 5393, 5689, 5903, 6029, 6173, 6653, 
    6977, 6997, 7451, 7507, 7727, 7993, 8629, 8663, 8887, 9041, 9323, 9623 ],
    [ 7, 37, 43, 47, 79, 103, 157, 163, 179, 181, 193, 197, 349, 389, 479, 487, 
    523, 673, 883, 953, 971, 1039, 1171, 1237, 1303, 1523, 1579, 1723, 1993, 
    2551, 2647, 2753, 2789, 2819, 2833, 3049, 3469, 3607, 3889, 4349, 4457, 
    4567, 4643, 5009, 5051, 5099, 5237, 5261, 5399, 5563, 5737, 6067, 6197, 
    6781, 6829, 7237, 7549, 8009, 8087, 8263, 8623, 8719, 9241 ],
    [ 43, 47, 53, 61, 71, 73, 89, 149, 241, 349, 373, 409, 419, 523, 557, 619, 
    641, 677, 683, 751, 761, 991, 1103, 1123, 1597, 1831, 1871, 2557, 2833, 
    4481, 4871, 5581, 5653, 7487, 9341, 9413, 9463, 9619, 9697, 9733 ],
    [ 7, 17, 37, 59, 61, 67, 79, 101, 107, 151, 197, 211, 227, 281, 421, 479, 
    487, 521, 523, 907, 941, 2141, 3323, 3371, 3673, 3691, 3701, 3793, 3821, 
    4241, 4783, 4831, 4877, 4919, 5003, 5147, 5507, 5557, 5857, 6079, 6793, 
    6959, 6983, 7211, 8389, 8501 ],
    [ 7, 17, 19, 23, 53, 61, 101, 109, 149, 157, 193, 227, 229, 317, 347, 359, 
    389, 461, 509, 521, 647, 797, 827, 857, 887, 1181, 1303, 1367, 1451, 1459, 
    1493, 1543, 1637, 1831, 1867, 2053, 2099, 2311, 2417, 2459, 2677, 2939, 
    2969, 3023, 3547, 4561, 4787, 4967, 6079, 6397, 6571, 6793, 6841, 7481, 
    7583, 7853, 8011, 8219, 8377, 9049, 9323, 9533, 9829, 9833 ],
    [ 43, 97, 139, 241, 379, 479, 1093, 1237, 1481, 1789, 2417, 2521, 6091, 
    8017, 8269, 8629, 9829 ],
    [ 23, 29, 73, 83, 127, 167, 181, 199, 283, 317, 331, 577, 661, 673, 727, 
    941, 1237, 1297, 1327, 2179, 2441, 3727, 3919, 3943, 4027, 4597, 5113, 5303,
    5851, 8761, 9187 ],
    [ 19, 41, 47, 59, 73, 79, 97, 103, 109, 137, 167, 191, 227, 229, 271, 307, 
    313, 359, 523, 577, 587, 647, 677, 827, 853, 1163, 1427, 1493, 1549, 1709, 
    1741, 1951, 2161, 2399, 2531, 2617, 2657, 2687, 2927, 3167, 3191, 3329, 
    3347, 3469, 3529, 3673, 3701, 3779, 3889, 4127, 4229, 4483, 4759, 4783, 
    4871, 4889, 4919, 5087, 5099, 5297, 5437, 5987, 6131, 6311, 6317, 6361, 
    6373, 6659, 7069, 7079, 7207, 7717, 7933, 8171, 8389, 8629, 8821, 9059, 
    9103, 9311, 9547, 9721, 9803, 9817, 9929 ],
    [ 3, 5, 11, 17, 23, 37, 41, 43, 47, 83, 89, 97, 103, 107, 151, 173, 197, 
    199, 227, 229, 353, 367, 379, 389, 397, 463, 479, 547, 563, 569, 571, 587, 
    727, 739, 769, 797, 907, 1153, 1249, 1367, 1499, 1511, 1627, 1657, 1951, 
    1999, 2011, 2207, 2281, 2393, 2437, 2477, 2543, 2777, 2797, 2927, 3169, 
    3181, 3343, 3413, 3449, 3529, 3559, 3631, 3793, 3803, 4289, 4423, 4483, 
    4517, 5153, 5189, 5297, 5347, 5669, 5867, 6121, 6689, 7127, 7523, 7549, 
    7583, 7717, 7919, 8467, 8741, 8779, 8819, 9257, 9551, 9679, 9769, 9817 ],
    [ 3, 5, 11, 29, 31, 43, 47, 79, 113, 131, 157, 167, 193, 223, 233, 239, 251,
    277, 317, 389, 463, 569, 577, 593, 613, 641, 769, 821, 883, 929, 947, 1013, 
    1061, 1187, 1217, 1327, 1361, 1433, 1559, 1579, 1613, 1811, 1913, 1973, 
    2087, 2251, 2417, 2551, 2557, 2719, 2753, 2819, 2909, 3061, 3191, 3203, 
    3361, 3371, 3391, 3643, 3671, 3769, 3833, 4201, 4241, 4243, 4273, 4337, 
    4409, 4451, 4691, 4721, 4729, 5039, 5099, 5231, 5521, 5651, 5689, 6151, 
    6917, 7523, 7829, 7927, 7963, 8167, 8179, 8719, 8969, 9109, 9323, 9623, 9929
    ],
    [ 3, 13, 17, 23, 41, 43, 61, 67, 71, 89, 131, 167, 191, 211, 239, 251, 331, 
    397, 409, 467, 541, 569, 617, 643, 677, 701, 751, 863, 941, 991, 1187, 1201,
    1229, 1327, 1447, 2297, 2351, 2969, 3089, 3457, 4007, 4177, 4261, 4283, 
    4363, 4481, 4517, 5449, 5563, 5749, 6043, 6689, 6793, 6871, 6899, 6917, 
    6977, 6991, 7727, 8171, 9643, 9749 ],
    [ 3, 5, 11, 13, 29, 31, 41, 43, 67, 71, 83, 89, 97, 113, 127, 131, 139, 151,
    173, 197, 211, 227, 239, 251, 281, 293, 307, 389, 449, 463, 491, 503, 521, 
    547, 587, 601, 617, 631, 659, 673, 701, 727, 743, 757, 761, 797, 827, 877, 
    881, 883, 911, 953, 1009, 1049, 1051, 1093, 1109, 1163, 1171, 1259, 1289, 
    1303, 1367, 1373, 1429, 1487, 1499, 1543, 1579, 1583, 1637, 1667, 1721, 
    1723, 1811, 1873, 1889, 2003, 2087, 2089, 2099, 2111, 2141, 2213, 2239, 
    2267, 2269, 2273, 2297, 2311, 2339, 2347, 2381, 2393, 2423, 2437, 2477, 
    2521, 2549, 2591, 2647, 2659, 2689, 2767, 2797, 2801, 2843, 2851, 2897, 
    2927, 2953, 3011, 3023, 3137, 3221, 3359, 3389, 3557, 3583, 3613, 3739, 
    3779, 3823, 3833, 3931, 4019, 4139, 4159, 4201, 4229, 4243, 4271, 4283, 
    4397, 4409, 4451, 4481, 4493, 4523, 4691, 4733, 4789, 4801, 4831, 5077, 
    5087, 5153, 5167, 5171, 5237, 5279, 5419, 5531, 5573, 5791, 5857, 5923, 
    5953, 6073, 6089, 6131, 6133, 6143, 6173, 6203, 6217, 6269, 6277, 6287, 
    6299, 6329, 6343, 6421, 6449, 6577, 6581, 6653, 6761, 6791, 6803, 6833, 
    6917, 6959, 7043, 7069, 7211, 7253, 7433, 7477, 7489, 7547, 7561, 7603, 
    7643, 7673, 7687, 7757, 7841, 7883, 8009, 8179, 8231, 8317, 8387, 8429, 
    8513, 8573, 8623, 8627, 8699, 8719, 8753, 8807, 8849, 8929, 8933, 9059, 
    9157, 9173, 9241, 9311, 9319, 9323, 9551, 9677, 9743, 9769, 9787, 9857, 
    9883, 9967 ],
    [ 3, 5, 11, 13, 23, 29, 41, 43, 71, 83, 89, 97, 113, 139, 163, 167, 173, 
    197, 223, 227, 251, 281, 293, 359, 367, 389, 419, 449, 503, 521, 523, 587, 
    601, 617, 631, 673, 701, 757, 761, 797, 811, 827, 839, 877, 881, 911, 953, 
    1009, 1049, 1063, 1091, 1093, 1109, 1259, 1289, 1373, 1399, 1427, 1429, 
    1447, 1499, 1523, 1567, 1637, 1721, 1847, 1873, 1889, 2039, 2087, 2089, 
    2099, 2141, 2213, 2239, 2267, 2269, 2273, 2287, 2297, 2339, 2351, 2381, 
    2393, 2423, 2437, 2477, 2521, 2531, 2549, 2591, 2659, 2687, 2689, 2797, 
    2801, 2803, 2843, 2897, 2953, 3011, 3067, 3079, 3137, 3163, 3221, 3299, 
    3319, 3359, 3389, 3463, 3499, 3557, 3613, 3779, 3833, 3851, 3863, 3947, 
    4003, 4019, 4201, 4229, 4283, 4397, 4409, 4447, 4481, 4493, 4507, 4523, 
    4651, 4703, 4733, 4759, 4787, 4789, 4801, 4903, 5011, 5039, 5077, 5153, 
    5237, 5303, 5347, 5431, 5531, 5573, 5651, 5711, 5807, 5851, 5857, 5953, 
    6073, 6089, 6131, 6133, 6151, 6173, 6217, 6269, 6271, 6277, 6299, 6329, 
    6421, 6449, 6551, 6577, 6581, 6653, 6691, 6761, 6827, 6833, 6917, 6959, 
    6971, 7069, 7253, 7433, 7477, 7489, 7561, 7673, 7699, 7727, 7757, 7841, 
    7883, 8009, 8087, 8179, 8231, 8317, 8429, 8513, 8573, 8623, 8699, 8753, 
    8819, 8849, 8929, 8933, 9157, 9173, 9239, 9241, 9323, 9463, 9677, 9743, 
    9769, 9857, 9883, 9967 ],
    [ 31, 163, 167, 193, 233, 263, 313, 349, 431, 443, 467, 569, 683, 1049, 
    1193, 1993, 2389, 3607, 4339, 4787, 5737, 6007, 6211, 6547, 7013, 9007 ],
    [ 13, 19, 23, 31, 41, 43, 113, 167, 223, 257, 457, 461, 467, 499, 563, 587, 
    683, 857, 1013, 1051, 1091, 1171, 1231, 1423, 1637, 1783, 1789, 1889, 1933, 
    2797, 2963, 3041, 3181, 3607, 3637, 3823, 4327, 4729, 4759, 5077, 5233, 
    5581, 5653, 6079, 8111, 8317, 8443, 9013, 9463, 9631, 9661, 9787, 9931 ]
];

// Mordell-Weil sieve primes computed with respect to the modulus (p1*p2*p3)^4

MWSPrimes := [
    [ 3, 23, 61, 173, 191, 193, 283, 431, 569, 6659, 7649, 8317, 8539 ],
    [ 23, 139, 701, 881, 1307, 1663, 1783, 7369, 8171, 8863, 9677 ],
    [ 13, 107, 179, 673, 8719 ],
    [ 1117, 1873, 1973, 2857, 2897, 3167, 8539, 9187, 9733 ],
    [ 3, 11, 19, 31, 83, 97, 101, 137, 139, 311, 317, 683, 733, 919, 991, 1409, 
    1579, 1663, 1697, 1823, 2063, 2749, 2789, 3373, 4057, 4337, 4519, 5153, 
    5167, 5237, 6563, 6661, 9011, 9277, 9631 ],
    [ 3, 5, 17, 37, 179, 263, 647, 727, 811, 1117, 1721, 1907, 2213, 2383, 2729,
    2789, 3319, 3467, 3491, 3499, 3701, 3847, 4259, 5039, 5639, 6143, 6719, 
    6827, 7177, 7517, 9127, 9413 ],
    [ 223, 359, 443, 557, 2129, 6607 ],
    [ 223, 359, 443, 557, 2129, 6607 ],
    [ 3, 29, 59, 107, 179, 199, 223, 229, 397, 409, 487, 607, 653, 757, 941, 
    947, 1193, 1319, 1429, 1699, 1999, 2297, 2371, 2693, 3533, 3833, 4391, 5039,
    5479, 5783, 6151, 7159, 7477, 7793, 7927, 8081, 8237, 8263, 9049, 9871 ],
    [ 11, 251, 487, 1543, 1801, 2111, 5897, 5927, 6599, 6793, 8263 ],
    [ 19, 557, 647, 4013, 7687, 8297 ],
    [ 11, 53, 251, 499, 541, 941, 1301, 1543, 3011, 3079, 4157, 4423, 4973, 8929
    ],
    [ 71, 1013, 2399, 3037, 5531, 7907 ],
    [ 71, 1873, 3167, 3517, 4157, 6067, 7283 ],
    [ 3, 359, 379, 457, 521, 1283, 2531, 2671, 2969, 4091, 4211, 5477, 5689, 
    6287, 6661, 8467, 9859 ],
    [ 13, 17, 101, 167, 223, 1861, 4733, 6689, 6967, 9539, 9929 ],
    [ 17, 103, 457, 547, 863, 3931, 4159, 5419, 5791, 6131, 6619 ],
    [ 3, 5, 137, 167, 191, 193, 199, 223, 233, 401, 467, 593, 661, 691, 701, 
    733, 809, 953, 967, 1051, 1109, 1699, 1847, 1907, 2129, 2153, 2741, 3163, 
    3307, 3461, 3541, 4391, 4463, 4597, 4861, 4931, 5563, 6029, 7309, 7451, 
    7621, 7993, 8123, 8837, 9323, 9689 ],
    [ 3, 11, 61, 83, 139, 167, 359, 499, 509, 751, 1187, 1667, 1699, 2633, 4889,
    4919, 6547 ],
    [ 3, 7, 181, 233, 1213, 1229, 1693, 1889, 3067, 3617, 4021, 4027, 4093, 
    5669, 5869, 8819 ],
    [ 41, 43, 101, 197, 251, 349, 541, 1291, 1543, 1669, 1801, 3319, 3329, 4133,
    4931, 6427, 9371 ],
    [ 3, 17, 41, 83, 139, 239, 541, 547, 823, 1697, 2531, 2917, 3889, 4933, 
    5189, 5407, 5839, 7283, 8737 ],
    [ 43, 167, 719, 1613, 2677, 2903, 4217, 5711, 5981 ],
    [ 3, 59, 101, 107, 127, 167, 293, 317, 433, 467, 479, 487, 547, 569, 601, 
    653, 677, 733, 739, 757, 883, 887, 907, 919, 1733, 1999, 2437, 2687, 2939, 
    3433, 3863, 4091, 4211, 4421, 5077, 5113, 5119, 5651, 6481, 6983, 7477, 
    8467, 8887, 9059, 9437 ],
    [ 7, 71, 79, 2843, 3413, 3779 ],
    [ 3, 97, 281, 293, 311, 347, 443, 521, 547, 569, 827, 829, 859, 883, 1019, 
    1061, 1201, 2543, 2663, 3167, 3187, 3463, 7211, 7591, 8017, 8171, 9829, 9907
    ],
    [ 19, 23, 139, 823, 1481, 1697, 2203, 3373, 4723, 7057, 7549, 8461, 8863, 
    9227 ],
    [ 7, 23, 67, 241, 883, 1259, 2617, 2729, 2797, 3529, 5407, 5867, 7039, 7451 
    ],
    [ 11, 19, 67, 71, 97, 107, 113, 317, 349, 373, 383, 467, 631, 727, 757, 809,
    983, 1187, 1193, 1213, 1223, 1237, 1451, 1627, 1663, 1759, 1811, 1901, 2017,
    2179, 2239, 2389, 2621, 2687, 2693, 2819, 4051, 5279, 5381, 5449, 5479, 
    5717, 6073, 6301, 6521, 7699, 8087, 8353, 8419, 9833 ],
    [ 3, 7, 97, 283, 461, 983, 2087, 2767, 2851, 3373, 3943, 4153, 5531, 5669, 
    6661, 7013, 7109, 8269, 8369, 8971 ],
    [ 503, 1291 ],
    [ 61, 197, 233, 421, 599, 941, 1291, 3079, 4973, 5897, 6619, 6793, 9749 ],
    [ 283 ],
    [ 3, 47, 67, 131, 137, 173, 179, 181, 211, 283, 313, 349, 487, 491, 523, 
    599, 947, 1879, 2633, 3167, 3187, 3677, 4001, 4567, 4703, 4937, 4967, 5953, 
    8117, 8713 ],
    [ 7, 107, 139, 149, 179, 227, 839, 853, 919, 1151, 2633, 3637, 4799, 6271, 
    8609 ],
    [ 3, 19, 43, 79, 107, 109, 277, 1213, 1319, 2063, 2347, 2617, 3319, 4561, 
    5021, 5233, 6451, 7517, 7699 ],
    [ 19, 47, 239, 823, 1033, 1201, 1213, 2909, 3467, 4967 ],
    [ 23, 137, 157, 251, 349, 499, 541, 1201, 1301, 1373, 1693, 1879, 2609, 
    4129, 4597, 4801, 5381, 6949, 8719, 9497 ],
    [ 3, 5, 29, 59, 71, 97, 149, 181, 191, 229, 251, 257, 269, 311, 317, 331, 
    353, 359, 383, 389, 431, 433, 577, 593, 647, 827, 947, 1021, 1213, 1229, 
    1321, 1409, 1433, 1453, 1571, 1619, 1721, 1787, 2161, 2377, 2399, 2621, 
    2749, 2969, 3271, 3323, 3371, 3449, 3469, 3491, 3529, 3659, 3727, 4129, 
    4657, 4877, 4933, 5261, 5531, 5641, 5669, 5749, 5857, 6301, 6473, 6791, 
    6899, 7127, 7499, 7517, 7577, 7583, 7589, 7829, 7907, 8017, 8171, 9157, 
    9277, 9521 ],
    [ 23, 457, 521, 2969, 3931, 5477, 5689, 6661, 7151, 8539 ],
    [ 19, 61, 71, 167, 173, 193, 307, 359, 569, 2251, 2531, 3359, 7649, 8317 ],
    [ 17, 151, 167, 577, 1171, 1663, 3257, 4259, 8951 ],
    [ 19, 683, 1621, 5953, 6199, 6359, 7369, 7549 ],
    [ 23, 67, 79, 107, 1439, 1823, 2693, 2729, 3019, 4789, 6143, 6673, 7537, 
    7723 ],
    [ 7, 83, 107, 241, 601, 883, 1063, 1259, 1601, 1619, 2011, 2383, 2617, 2729,
    3559, 5683, 6163, 8747, 9967 ],
    [ 3, 19, 29, 43, 71, 89, 239, 257, 271, 307, 379, 487, 617, 977, 997, 1439, 
    1861, 2939, 2969, 4013, 4567, 6269, 6947, 7537 ],
    [ 3, 11, 331, 491, 809, 821, 907, 1217, 1511, 1663, 1759, 3467, 3533, 3623, 
    4013, 4327, 4363, 5059, 5641, 7027, 7507, 7547, 7643, 8311 ],
    [ 7, 67, 271, 743, 1129, 2131, 4817, 6389 ],
    [ 11, 13, 17, 103, 347, 401, 457, 829, 863, 1163, 1889, 3469, 5791 ],
    [ 137, 269, 317, 487, 757, 1289, 4241, 6529, 8123 ],
    [ 223, 557, 599, 1901, 6449, 9157 ],
    [ 3, 13, 23, 107, 157, 397, 971, 1201, 1669, 1699, 1823, 2663, 4621, 4751, 
    4973, 6397, 7723, 8539 ],
    [ 3, 7, 41, 389, 541, 727, 751, 1031, 1667, 2221, 6529, 9601 ],
    [ 103, 1543, 1973, 8009, 9941 ],
    [ 67, 5569, 7741, 8783, 9091 ],
    [ 3, 7, 13, 107, 197, 223, 269, 587, 787, 839, 2243, 3529, 4099, 4933, 5839,
    6619, 6883, 9391 ],
    [ 7, 17, 41, 541, 1697, 2531, 2917, 3889, 4219, 4933, 5189, 5843, 8737, 8803
    ],
    [ 23, 71, 277, 1327, 1733, 1873, 2617, 3191, 4363, 6287, 7573, 7583, 8623 ],
    [ 661, 1319, 4129 ],
    [ 13, 23, 359, 1087, 2341, 2741, 3259, 3889, 9007 ],
    [ 3, 19, 103, 239, 443, 503, 601, 631, 641, 733, 2447, 2903, 3209, 3529, 
    6451, 7717, 7829, 8929 ],
    [ 227, 1193, 8363 ],
    [ 23, 31, 139, 251, 1481, 1697, 1783, 3373, 7057, 7549, 8461 ],
    [ 37, 491, 587, 881, 1259, 2797, 3469, 3833, 4079, 6089 ],
    [ 5, 7, 53, 67, 191, 239, 241, 271, 1987, 2267, 2389, 2417, 2447, 3907, 
    4057, 6607, 8677 ],
    [ 3, 19, 29, 53, 127, 173, 233, 347, 419, 431, 503, 613, 787, 809, 883, 
    1193, 1279, 1307, 1543, 1741, 2113, 2237, 2269, 2467, 3079, 3571, 4001, 
    6703, 6827, 9677 ],
    [ 13, 103, 163, 167, 233, 271, 1597, 1747, 2531, 3433, 3559, 3923, 3931, 
    4933, 5189, 6361, 6469, 8069 ],
    [ 181, 197, 239, 547, 787, 839, 937, 1163, 1747, 1889, 1997, 2677, 3931, 
    4933, 4951, 5839, 5939, 5981, 6619, 8387 ],
    [ 19, 41, 197, 1783, 2903, 4003, 5167 ],
    [ 3, 5, 19, 47, 53, 59, 79, 89, 103, 107, 241, 263, 281, 293, 349, 373, 433,
    439, 443, 607, 613, 619, 787, 809, 857, 877, 883, 1181, 1409, 1789, 1847, 
    1901, 2237, 2543, 2617, 2621, 2887, 2953, 3457, 3469, 3797, 4049, 4283, 
    4649, 5557, 5647, 5923, 6079, 6163, 6553, 6781, 7351, 7487, 8017, 8221, 
    8353, 8461, 9049, 9157, 9209, 9973 ],
    [ 79, 4177, 7079, 9323 ],
    [ 3, 29, 31, 71, 107, 397, 401, 643, 743, 797, 929, 937, 1249, 2311, 3517, 
    3613, 6977, 7687, 7927 ],
    [ 19, 59, 503, 1091, 2687, 3931, 4051, 7691, 9437, 9677, 9679 ],
    [ 71, 431, 1277, 1429 ],
    [ 31, 227, 4423, 8093 ],
    [ 127, 521, 523, 2971, 3209, 8731 ],
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    [ 43, 107, 359, 491, 787, 1783, 1877, 2137, 8081, 8677, 8963, 9623 ],
    [ 23, 53, 313, 359, 571, 7853, 9721 ],
    [ 1511 ],
    [ 17, 421, 1181, 1609, 6967 ],
    [ 3, 5, 7, 23, 31, 37, 61, 79, 83, 103, 149, 163, 227, 257, 271, 277, 419, 
    557, 673, 683, 773, 859, 929, 941, 997, 1193, 1777, 3191, 3761, 3947, 4357, 
    4421, 4447, 4517, 4969, 5689, 6047, 6067, 6197, 6571, 6673, 6679, 6857, 
    7507, 7559, 7717, 8689, 9283, 9311 ],
    [ 1483, 8329 ],
    [ 19, 409, 1327, 1511, 8783, 8837, 9413, 9619, 9839 ],
    [ 7, 11, 41, 61, 67, 71, 101, 113, 317, 653, 659, 709, 727, 1013, 1019, 
    1033, 1523, 2011, 2069, 3037, 3331, 4211, 5743, 6563, 7951, 8467, 9719, 9887
    ],
    [ 11, 23, 107, 109, 193, 419, 1021, 1433, 8171 ],
    [ 7, 19, 149, 181, 409, 1297, 1307, 1381, 2683, 3581, 3719, 4127, 4229, 
    7673, 8011, 9221, 9277, 9397 ],
    [ 3, 11, 23, 109, 193, 1019, 1021, 1433, 2347, 3319, 4703, 6323, 6659, 8699 
    ],
    [ 149, 181, 211, 271, 409, 443, 463, 1087, 1297, 1381, 2339, 2351, 2411, 
    2971, 3539, 3581, 3659, 4003, 4019, 4229, 5519, 7673, 8011, 8171, 8863, 
    9221, 9277, 9397 ],
    [ 3, 5, 23, 37, 41, 59, 71, 113, 149, 157, 197, 211, 239, 263, 307, 467, 
    797, 839, 977, 1249, 1319, 1433, 1453, 2311, 3079, 3833, 3863, 4027, 4481, 
    5743, 8387, 8627, 8741, 9473 ],
    [ 5417 ],
    [ 541, 773, 1307, 2417, 3671, 5711, 5801, 5851, 9601 ],
    [ 19, 659, 853, 947, 4813 ],
    [ 71, 149, 241, 661, 2141, 2797, 3413, 3847, 4127, 4271 ],
    [ 3, 13, 17, 59, 67, 83, 101, 109, 137, 149, 277, 307, 317, 397, 433, 463, 
    491, 571, 577, 601, 769, 1129, 1283, 1297, 1327, 1451, 1453, 1663, 1999, 
    2437, 3061, 3079, 3559, 3851, 4027, 4049, 4201, 4219, 4327, 4337, 4723, 
    5651, 7177, 7459, 8467, 9091, 9133, 9157, 9749 ],
    [ 6101 ],
    [ 1319, 5923 ],
    [ 31, 43, 53, 83, 181, 331, 467, 487, 1933, 2309, 3413, 6869, 8599 ],
    [ 3, 97, 109, 131, 523, 859, 1051, 1721, 1933, 2377, 2423, 2473, 4327, 8747 
    ],
    [ 13, 43, 103, 193, 263, 431, 577, 709, 857, 1999, 2393, 2467, 3389, 5801, 
    6779 ],
    [ 3, 5, 23, 167, 229, 349, 467, 1051, 1061, 1201, 1487, 1499, 1579, 1759, 
    1907, 2089, 2129, 2137, 2663, 3617, 3769, 3931, 4057, 4297, 4451, 5507, 
    5737, 7433, 7499, 8123, 9341 ],
    [ 3, 5, 23, 47, 67, 127, 139, 191, 229, 349, 691, 1031, 1061, 1201, 1279, 
    1583, 2089, 2129, 2137, 3307, 3617, 3769, 4057, 4297, 4391, 5507, 5737, 
    7433, 9341 ],
    [ 11, 43, 101, 251, 599, 1801, 2693, 3253, 3301, 4973, 6287, 6547, 6599, 
    6863, 7549, 7603, 8521, 9371 ],
    [ 3, 29, 41, 43, 263, 823, 953, 1447, 1777, 2713, 3329, 5273, 6761, 8819 ],
    [ 2347, 8069 ],
    [ 3, 97, 181, 227, 283, 461, 1229, 1607, 2179, 3037, 4021, 6661, 8819 ],
    [ 29, 1483, 2287, 5749 ],
    [ 19, 167, 1549, 1613, 2903, 6343, 6709 ],
    [ 3, 5, 13, 29, 41, 71, 149, 167, 499, 569, 641, 1249, 1307, 1423, 1459, 
    1499, 1913, 2591, 3209, 3821, 4463, 9661 ],
    [ 83, 2083, 2699, 4391, 5749 ],
    [ 5, 41, 73, 109, 569, 881, 2447, 3673, 6089, 6581, 6719, 6863, 8737, 9811 
    ],
    [ 71, 79, 1399, 4943, 6359 ],
    [ 13, 17, 283, 313, 911, 1051, 1723, 2383, 2437, 2939, 4261 ],
    [ 449, 641, 661, 4261, 4463 ],
    [ 193, 199, 523, 691, 3371, 3889, 4133 ],
    [ 3, 5, 37, 41, 43, 83, 113, 151, 353, 379, 569, 587, 727, 887, 947, 1063, 
    1499, 1511, 1583, 1777, 2797, 2857, 3331, 3803, 4423, 4483, 6689, 7283, 
    7333, 7481, 9391 ],
    [ 79, 467, 701, 821, 877, 1123, 1151, 1447, 1877, 7213 ],
    [ 433, 541, 547, 569, 937, 1039, 1453, 1583, 2351, 2467, 2633, 3559, 3923, 
    4099, 5449, 6619, 6907, 8737 ],
    [ 19, 29, 61, 149, 613, 829, 1181, 1637, 1699, 1709, 2039, 2447, 2789, 4261,
    4481, 5657, 5849, 6101, 7349, 7433, 8269, 8513, 9421 ],
    [ 3, 19, 47, 197, 199, 347, 379, 419, 431, 479, 619, 677, 719, 787, 829, 
    839, 859, 919, 1093, 1187, 1193, 1289, 1399, 2473, 2503, 2663, 2711, 2939, 
    3209, 3323, 3511, 3761, 4001, 4253, 4327, 6521, 7001, 9923 ],
    [ 97, 241, 463, 487, 1237, 1481, 1531, 1789, 2417, 2521, 8017, 8629, 9787, 
    9811, 9829 ],
    [ 2099, 2161, 8537 ],
    [],
    [ 13, 127, 191, 509, 877, 1277, 1823, 2917, 3061, 4517, 7027, 7129, 8123 ],
    [ 97, 199, 647, 739, 1277, 2161, 3373, 4127, 4721, 7417, 7901 ],
    [ 11, 83, 107, 239, 271, 463, 491, 563, 773, 1091, 1319, 1499, 1889, 3373, 
    3929, 6143, 6569, 8677, 8699 ],
    [ 3, 7, 17, 101, 521, 643, 677, 683, 809, 2027, 2081, 2689, 2741, 3061, 
    3259, 3361, 3931, 5399, 5651, 6661, 6781, 7481, 7669, 9323, 9551 ],
    [ 83, 3251 ],
    [ 5, 23, 157, 167, 257, 347, 619, 809, 883, 911, 1237, 1279, 1297, 1607, 
    1721, 1889, 2111, 2309, 2833, 3067, 3209, 3329, 3347, 3593, 3701, 3917, 
    4547, 4943, 5639, 6143, 6277, 6827, 7057, 7177, 7451 ],
    [ 3, 5, 13, 23, 37, 89, 137, 191, 223, 233, 313, 353, 467, 593, 733, 757, 
    991, 1061, 1153, 1487, 1699, 1907, 1913, 2089, 2221, 2243, 3137, 3323, 4057,
    4243, 4357, 6553, 7309, 7529, 8039 ],
    [ 11, 43, 71, 131, 331, 349, 541, 967, 977, 1801, 2657, 2857, 3011, 4423, 
    5527, 6619, 7621 ],
    [ 103, 1213, 2663, 8719 ],
    [ 241, 2063, 6761, 7723 ],
    [ 311, 557, 839, 5861 ],
    [ 661, 1097, 1237 ],
    [ 79, 97, 103, 127, 157, 193, 197, 293, 373, 401, 409, 433, 449, 727, 751, 
    809, 877, 929, 977, 1009, 1013, 1091, 1117, 1553, 1601, 1663, 1693, 1889, 
    1997, 2017, 2113, 2161, 2287, 2797, 3529, 3697, 3733, 4027, 4283, 4969, 
    5441, 6089, 6199, 7057, 7121, 7681, 7841, 7873, 9157, 9551 ],
    [ 11, 23, 101, 113, 167, 709, 719, 863, 1453, 2017, 2237, 6949 ],
    [ 19, 43, 113, 137, 163, 239, 251, 263, 271, 283, 563, 593, 701, 739, 797, 
    823, 827, 1213, 1283, 1321, 1373, 1783, 1877, 1889, 2137, 2357, 2729, 3229, 
    4663, 6173, 7417, 8017, 8893, 9281, 9623 ],
    [ 3, 5, 73, 109, 227, 229, 241, 251, 347, 433, 457, 647, 677, 947, 1019, 
    1093, 1193, 1223, 1291, 1489, 1493, 1871, 1997, 2083, 2141, 5531, 6607, 
    7103, 7321, 7753, 8597, 8941, 9377 ],
    [ 3, 5, 7, 23, 31, 37, 47, 61, 79, 83, 131, 149, 227, 257, 277, 419, 463, 
    557, 607, 673, 773, 859, 863, 929, 941, 997, 1193, 1531, 1777, 1787, 1931, 
    2399, 3761, 4357, 4421, 4517, 4969, 5387, 5689, 6197, 6311, 6673, 6857, 
    6967, 7717, 8689 ],
    [ 31, 409, 8837, 9413, 9619 ],
    [ 7, 17, 19, 41, 89, 233, 1229, 2113, 2383, 2801, 4271, 4297, 9467 ],
    [ 29, 61, 137, 151, 457, 1213, 2029, 2371, 2399, 6079, 6151, 9467 ],
    [ 3, 5, 23, 89, 103, 139, 367, 379, 383, 433, 509, 631, 647, 911, 1021, 
    1321, 1559, 1571, 1619, 1721, 1747, 2161, 2281, 2377, 2579, 2633, 2731, 
    3067, 3371, 3491, 3719, 3727, 4327, 4657, 4751, 4877, 4967, 5507, 5531, 
    5641, 5879, 6521, 7489, 7499, 7517, 7547, 7907, 8017, 8171, 9157, 9241, 9277
    ],
    [ 41, 53, 71, 449, 2677, 4091, 4657, 7853, 9157 ],
    [ 7, 19, 83, 229, 367, 593, 599, 601, 661, 883, 887, 1193, 1223, 1277, 1753,
    2707, 2729, 3187, 4157, 5147, 6703, 6971 ],
    [ 5, 7, 19, 43, 107, 131, 191, 601, 1277, 1697, 2707, 2843, 3847, 5623, 
    5869, 6577, 6703 ],
    [ 3, 97, 307, 311, 2437, 3793, 6257 ],
    [ 127, 181, 229, 331, 347, 877, 991, 1013, 1021, 1301, 1481, 2143, 2267, 
    4273, 4349, 5507, 5981, 6113, 6469, 7121 ],
    [ 3, 139, 157, 947, 971, 1381, 2579, 4211, 4721, 5153, 9437, 9901 ],
    [ 11, 13, 157, 257, 773, 1381, 2687, 3083, 3329, 3467, 3557, 4463, 5303, 
    7691 ],
    [ 23, 59, 109, 233, 251, 293, 523, 617, 641, 1021, 1181, 1367, 1433, 1549, 
    2789, 3023, 3769, 3779, 4583, 4729, 5521, 7019, 7459, 9059 ],
    [ 5, 197, 613, 863, 5591, 6619, 6863, 8501, 9883 ],
    [ 3, 5, 29, 31, 43, 59, 89, 107, 149, 179, 211, 223, 263, 281, 311, 331, 
    433, 439, 443, 457, 487, 599, 751, 1013, 1091, 1249, 1381, 1613, 1847, 1879,
    1901, 2237, 2341, 2417, 2729, 2791, 2857, 3023, 3793, 3947, 4133, 4423, 
    4507, 4621, 5087, 5323, 5557, 5563, 5581, 6229, 6553, 6791, 7333, 7549, 
    7993, 8017, 8111, 8293, 8623, 8971, 9049, 9421, 9973 ],
    [ 53, 181, 1933, 2309, 3413, 6869 ],
    [ 11, 89, 239, 313, 379, 457, 761, 937, 953, 1201, 2297, 2473, 2657, 2713, 
    3449, 3907, 4651, 5179, 5897, 6619, 6691, 7043, 7187, 7283, 7937, 8161 ],
    [ 89, 1279, 1303, 5813 ],
    [ 13, 113, 307, 709, 797, 1999, 2707, 3067, 7219, 7523, 8231 ],
    [ 3, 5, 7, 11, 29, 59, 83, 101, 109, 167, 179, 463, 499, 593, 631, 733, 809,
    953, 1039, 1109, 1627, 1699, 1823, 1879, 2153, 2293, 2477, 2741, 2843, 3023,
    3253, 3347, 3761, 4027, 4421, 4447, 4463, 4783, 5153, 6397, 6997, 8161, 
    9007, 9323 ],
    [ 5, 59, 241, 271, 1223, 1567, 3541, 3701, 4799 ],
    [],
    [ 13, 17, 103, 107, 139, 241, 541, 547, 587, 887, 1181, 2213, 2531, 2713, 
    3469, 5281, 6269, 6653, 6949, 7283, 7457, 7823 ],
    [ 23, 251, 593, 613, 967, 1823, 2689, 2917, 4649, 5701, 8243, 8867 ],
    [ 467, 727, 1307, 1663, 2053, 2777, 3319 ],
    [ 41, 53, 131, 197, 313, 641, 1259, 1303, 2683, 2803, 4013, 6221 ],
    [ 61, 379, 409, 491, 683, 863, 1373, 1567, 1997, 2087, 2861, 5023, 7451, 
    7649 ],
    [ 11, 137, 179, 211, 541, 599, 619, 977, 1117, 1187, 1543, 3329, 3793, 6037,
    7187, 7867, 8117, 8761 ],
    [ 3, 5, 7, 29, 31, 59, 97, 167, 199, 223, 233, 401, 499, 571, 593, 599, 631,
    719, 953, 967, 1109, 1847, 2083, 2153, 2687, 2713, 2843, 3229, 3581, 3623, 
    3631, 4001, 4013, 4751, 4919, 6173, 6997, 7451, 7727, 7993 ],
    [ 7, 179, 193, 523, 1039, 1237, 1579, 1723, 2647, 2833, 5099, 6781, 6829, 
    8719, 9241 ],
    [ 677, 761, 1123, 1597, 5653, 9413 ],
    [ 7, 17, 61, 67, 151, 487, 521, 3673, 3691, 3821, 4877, 5557, 5857, 6793, 
    8389 ],
    [ 7, 17, 53, 61, 101, 109, 149, 157, 317, 347, 359, 797, 827, 857, 1493, 
    1831, 2417, 2459, 2677, 3023, 4561, 4787, 6397, 7853 ],
    [ 43, 97, 241, 1237, 1481, 1789, 2417, 2521, 6091, 8017, 8629, 9829 ],
    [ 73, 3943 ],
    [ 79, 97, 103, 137, 229, 1427, 5437, 8171, 8389, 9059, 9547 ],
    [ 3, 5, 11, 41, 43, 107, 151, 173, 199, 227, 353, 379, 547, 569, 571, 907, 
    1367, 1627, 2011, 2777, 2797, 2927, 3169, 3413, 4289, 4423, 4483, 4517, 
    5153, 5297, 6121, 7127, 7717, 8467, 8779, 9257 ],
    [ 3, 11, 31, 113, 131, 239, 389, 641, 821, 883, 1013, 1187, 1217, 1361, 
    1613, 1973, 2251, 3061, 3361, 3769, 3833, 4273, 4409, 4451, 4691, 4729, 
    5231, 5689, 6151, 6917, 7523, 7927, 8167, 8179, 9323 ],
    [ 3, 13, 17, 23, 71, 131, 167, 191, 239, 409, 1187, 1229, 2969, 4177, 4261, 
    4363, 5749, 6689, 6899 ],
    [ 3, 5, 11, 29, 31, 67, 89, 113, 131, 151, 173, 197, 211, 227, 293, 389, 
    521, 547, 587, 631, 659, 673, 701, 743, 761, 877, 881, 953, 1109, 1171, 
    1259, 1289, 1303, 1367, 1487, 1543, 1579, 1583, 1637, 1811, 1873, 1889, 
    2003, 2089, 2111, 2213, 2239, 2269, 2273, 2297, 2339, 2347, 2477, 2521, 
    2549, 2591, 2647, 2689, 2767, 2797, 2801, 2851, 3359, 3613, 3823, 3833, 
    3931, 4019, 4139, 4243, 4271, 4397, 4409, 4691, 4733, 4801, 4831, 5077, 
    5087, 5171, 5419, 5791, 5857, 5923, 5953, 6073, 6131, 6143, 6269, 6277, 
    6329, 6421, 6449, 6577, 6653, 6959, 7043, 7069, 7211, 7253, 7433, 7547, 
    7561, 7603, 7687, 7757, 7841, 8179, 8317, 8573, 8627, 8699, 8719, 8753, 
    8929, 9173, 9319, 9551, 9677, 9769, 9787, 9883, 9967 ],
    [ 3, 5, 11, 23, 29, 89, 113, 163, 167, 173, 197, 223, 227, 293, 359, 367, 
    389, 521, 523, 673, 701, 761, 827, 877, 881, 953, 1063, 1091, 1109, 1289, 
    1447, 1523, 1637, 1873, 1889, 2039, 2087, 2089, 2213, 2269, 2273, 2287, 
    2297, 2423, 2477, 2521, 2531, 2549, 2591, 2659, 2687, 2689, 2797, 2801, 
    2803, 3011, 3163, 3299, 3319, 3463, 3613, 3833, 3863, 4283, 4397, 4409, 
    4447, 4523, 4651, 4733, 4759, 4801, 4903, 5077, 5303, 5347, 5651, 5807, 
    5857, 5953, 6073, 6151, 6269, 6277, 6329, 6421, 6449, 6551, 6577, 6653, 
    6691, 6827, 7069, 7253, 7433, 7561, 7699, 7757, 7841, 8087, 8179, 8317, 
    8573, 8623, 8699, 8753, 8929, 9173, 9463, 9677, 9743, 9769 ],
    [ 313, 467, 569, 1193, 3607, 7013 ],
    [ 13, 19, 43, 1171, 1231, 1423, 1637, 1783, 1889, 2797, 3041, 3637, 4327, 
    4759, 5077, 5233, 8443, 9661 ]
];

// Mordell-Weil sieve primes computed with respect to the modulus 2*(p1*p2*p3)^4

MWSPrimes2 := [
    [ 3, 23, 61, 67, 107, 113, 173, 191, 193, 239, 283, 431, 467, 569, 823, 971,
    1283, 1597, 2927, 3517, 3607, 5039, 6659, 7151, 7649, 8317, 8539 ],
    [ 19, 23, 139, 191, 367, 701, 733, 881, 887, 1019, 1249, 1307, 1439, 1663, 
    1697, 1747, 1753, 1783, 2957, 6047, 6343, 7057, 7369, 8117, 8171, 8831, 
    8863, 9277, 9677 ],
    [ 13, 89, 107, 179, 223, 397, 673, 1759, 3499, 4817, 6451, 8719, 8803 ],
    [ 17, 311, 823, 1117, 1873, 1973, 2309, 2857, 2897, 3167, 3631, 6217, 6287, 
    7151, 8317, 8539, 9187, 9733 ],
    [ 3, 11, 19, 29, 31, 47, 59, 79, 83, 97, 101, 137, 139, 199, 223, 311, 317, 
    397, 421, 461, 467, 577, 647, 683, 701, 733, 797, 919, 991, 1409, 1439, 
    1481, 1579, 1597, 1663, 1669, 1697, 1723, 1823, 1979, 1997, 2053, 2063, 
    2377, 2609, 2713, 2749, 2789, 2957, 3049, 3181, 3373, 3511, 3643, 3803, 
    4001, 4049, 4057, 4259, 4337, 4441, 4519, 4621, 5153, 5167, 5237, 5297, 
    5449, 5479, 5683, 5953, 6247, 6367, 6473, 6563, 6661, 7057, 7639, 8609, 
    9011, 9277, 9631 ],
    [ 3, 5, 17, 19, 29, 37, 97, 157, 167, 179, 257, 263, 269, 271, 317, 409, 
    461, 491, 593, 613, 643, 647, 727, 811, 1013, 1097, 1117, 1237, 1289, 1433, 
    1451, 1453, 1499, 1601, 1721, 1907, 2141, 2161, 2213, 2269, 2383, 2711, 
    2713, 2729, 2789, 2969, 3083, 3319, 3467, 3491, 3499, 3691, 3701, 3847, 
    4259, 4457, 4591, 4657, 4663, 5039, 5333, 5639, 6143, 6709, 6719, 6827, 
    7057, 7177, 7517, 7873, 7901, 8311, 8893, 8929, 9127, 9257, 9413 ],
    [ 223, 317, 347, 359, 443, 557, 887, 1697, 2129, 2833, 6607 ],
    [ 223, 317, 347, 359, 443, 557, 887, 1697, 2129, 2833, 6607 ],
    [ 3, 7, 11, 23, 29, 31, 47, 59, 61, 67, 71, 79, 107, 131, 139, 149, 151, 
    163, 179, 181, 193, 199, 211, 223, 229, 233, 269, 281, 311, 313, 367, 397, 
    409, 457, 479, 487, 499, 607, 653, 659, 661, 743, 751, 757, 797, 857, 919, 
    937, 941, 947, 1021, 1031, 1163, 1193, 1249, 1289, 1319, 1381, 1423, 1429, 
    1439, 1667, 1699, 1907, 1999, 2063, 2239, 2267, 2297, 2339, 2347, 2371, 
    2693, 2789, 2909, 3041, 3217, 3221, 3371, 3511, 3533, 3691, 3697, 3833, 
    3851, 4349, 4391, 4621, 4651, 4759, 4831, 4967, 5039, 5051, 5113, 5227, 
    5477, 5479, 5651, 5737, 5779, 5783, 5879, 5927, 6079, 6151, 6197, 6211, 
    6337, 6379, 6451, 6491, 6709, 6899, 7013, 7159, 7207, 7349, 7477, 7537, 
    7687, 7699, 7793, 7879, 7907, 7927, 8081, 8237, 8243, 8263, 8389, 8971, 
    9049, 9221, 9871 ],
    [ 11, 101, 179, 181, 197, 251, 271, 487, 571, 619, 1009, 1499, 1543, 1579, 
    1801, 2111, 3167, 3797, 4657, 5749, 5897, 5927, 6599, 6793, 6949, 7649, 
    7703, 8263 ],
    [ 19, 191, 557, 647, 1663, 1709, 2833, 3907, 4013, 7687, 8297, 9803 ],
    [ 11, 53, 181, 211, 251, 499, 541, 661, 941, 967, 1213, 1301, 1523, 1543, 
    2699, 3011, 3079, 3167, 3677, 3797, 3863, 4157, 4423, 4973, 5011, 5779, 
    6949, 7703, 8273, 8929 ],
    [ 71, 109, 233, 499, 1013, 1439, 1571, 2399, 3037, 4481, 4967, 5531, 7907, 
    8171, 9521, 9901 ],
    [ 61, 71, 1873, 3163, 3167, 3517, 4157, 5437, 6067, 6883, 7283 ],
    [ 3, 17, 19, 43, 61, 113, 359, 379, 383, 457, 521, 643, 1031, 1069, 1163, 
    1229, 1283, 1553, 1597, 2131, 2383, 2473, 2531, 2593, 2671, 2969, 4091, 
    4211, 4261, 5477, 5689, 6287, 6661, 6781, 6883, 8233, 8317, 8467, 9859, 9887
    ],
    [ 13, 17, 101, 167, 193, 223, 271, 421, 677, 853, 1609, 1861, 2179, 2311, 
    4733, 6221, 6689, 6967, 9539, 9929 ],
    [ 17, 103, 107, 277, 457, 541, 547, 557, 761, 863, 937, 2161, 2243, 3931, 
    4159, 5419, 5791, 6131, 6619, 7283, 8101 ],
    [ 3, 5, 31, 37, 67, 73, 83, 131, 137, 167, 191, 193, 199, 223, 233, 311, 
    313, 331, 401, 467, 499, 569, 593, 661, 691, 701, 719, 733, 773, 809, 937, 
    953, 967, 1031, 1039, 1051, 1109, 1663, 1699, 1709, 1831, 1847, 1901, 1907, 
    1913, 2129, 2153, 2741, 3089, 3163, 3307, 3413, 3461, 3541, 3769, 4357, 
    4391, 4457, 4463, 4597, 4651, 4861, 4931, 5563, 5903, 5939, 6029, 6361, 
    6653, 7151, 7309, 7451, 7621, 7993, 8123, 8623, 8629, 8837, 8887, 9323, 
    9689, 9901 ],
    [ 3, 11, 31, 43, 61, 83, 139, 167, 181, 193, 223, 311, 313, 359, 499, 509, 
    719, 727, 733, 751, 1039, 1187, 1667, 1699, 1709, 2341, 2357, 2609, 2633, 
    2729, 3319, 3659, 4751, 4889, 4919, 6029, 6547, 8623 ],
    [ 3, 7, 181, 233, 277, 401, 1019, 1087, 1213, 1229, 1439, 1621, 1693, 1889, 
    3067, 3253, 3373, 3571, 3617, 3943, 4021, 4027, 4093, 4457, 5669, 5869, 
    6661, 7333, 8363, 8819, 9901 ],
    [ 23, 41, 43, 101, 103, 157, 197, 227, 251, 349, 541, 733, 1117, 1291, 1301,
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