/*
 * java-math-library is a Java library focused on number theory, but not necessarily limited to it. It is based on the PSIQS 4.0 factoring project.
 * Copyright (C) 2018 Tilman Neumann (www.tilman-neumann.de)
 *
 * This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License
 * as published by the Free Software Foundation; either version 3 of the License, or (at your option) any later version.
 *
 * This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied
 * warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.
 *
 * You should have received a copy of the GNU General Public License along with this program;
 * if not, see <http://www.gnu.org/licenses/>.
 */
package de.tilman_neumann.jml.primes.probable;

import static de.tilman_neumann.jml.base.BigIntConstants.*;

import java.math.BigInteger;
import java.util.HashSet;

/**
 * BPSW probable prime test. The implementation starts checking the moduli of N % 30030 and then follows
 * [http://en.wikipedia.org/wiki/Baillie-PSW_primality_test] and references therein.
 * 
 * Note that BPSW may be considered a deterministic prime test for N < 2^64.
 * 
 * @author Tilman Neumann
 */
public class BPSWTest {
	/** 2*3*5*7*11*13 = 30030 */
	private static final BigInteger BIG_30030 = BigInteger.valueOf(30030);

	/** 5760 rests of primes % (2*3*5*7*11*13) */
	private static HashSet<Integer> primeRestsMod30030 = toHashSet(new int[] {1, 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, 289, 293, 307, 311, 313, 317, 323, 331, 337, 347, 349, 353, 359, 361, 367, 373, 379, 383, 389, 391, 397, 401, 409, 419, 421, 431, 433, 437, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 493, 499, 503, 509, 521, 523, 527, 529, 541, 547, 551, 557, 563, 569, 571, 577, 587, 589, 593, 599, 601, 607, 613, 617, 619, 629, 631, 641, 643, 647, 653, 659, 661, 667, 673, 677, 683, 691, 697, 701, 703, 709, 713, 719, 727, 731, 733, 739, 743, 751, 757, 761, 769, 773, 779, 787, 797, 799, 809, 811, 817, 821, 823, 827, 829, 839, 841, 851, 853, 857, 859, 863, 877, 881, 883, 887, 893, 899, 901, 907, 911, 919, 929, 937, 941, 943, 947, 953, 961, 967, 971, 977, 983, 989, 991, 997, 1003, 1007, 1009, 1013, 1019, 1021, 1031, 1033, 1037, 1039, 1049, 1051, 1061, 1063, 1069, 1073, 1081, 1087, 1091, 1093, 1097, 1103, 1109, 1117, 1121, 1123, 1129, 1139, 1147, 1151, 1153, 1159, 1163, 1171, 1181, 1187, 1189, 1193, 1201, 1207, 1213, 1217, 1219, 1223, 1229, 1231, 1237, 1241, 1247, 1249, 1259, 1271, 1273, 1277, 1279, 1283, 1289, 1291, 1297, 1301, 1303, 1307, 1319, 1321, 1327, 1333, 1343, 1349, 1357, 1361, 1363, 1367, 1369, 1373, 1381, 1387, 1399, 1403, 1409, 1411, 1423, 1427, 1429, 1433, 1439, 1447, 1451, 1453, 1457, 1459, 1471, 1481, 1483, 1487, 1489, 1493, 1499, 1501, 1511, 1513, 1517, 1523, 1531, 1537, 1541, 1543, 1549, 1553, 1559, 1567, 1571, 1577, 1579, 1583, 1591, 1597, 1601, 1607, 1609, 1613, 1619, 1621, 1627, 1633, 1637, 1643, 1649, 1657, 1663, 1667, 1669, 1679, 1681, 1691, 1693, 1697, 1699, 1709, 1711, 1717, 1721, 1723, 1733, 1739, 1741, 1747, 1751, 1753, 1759, 1763, 1769, 1777, 1783, 1787, 1789, 1801, 1811, 1817, 1819, 1823, 1829, 1831, 1843, 1847, 1849, 1853, 1861, 1867, 1871, 1873, 1877, 1879, 1889, 1891, 1901, 1907, 1909, 1913, 1919, 1921, 1927, 1931, 1933, 1943, 1949, 1951, 1957, 1961, 1973, 1979, 1987, 1993, 1997, 1999, 2003, 2011, 2017, 2021, 2027, 2029, 2033, 2039, 2047, 2053, 2059, 2063, 2069, 2071, 2077, 2081, 2083, 2087, 2089, 2099, 2111, 2113, 2117, 2129, 2131, 2137, 2141, 2143, 2147, 2153, 2159, 2161, 2173, 2179, 2183, 2201, 2203, 2207, 2209, 2213, 2221, 2227, 2231, 2237, 2239, 2243, 2251, 2257, 2263, 2267, 2269, 2273, 2279, 2281, 2287, 2291, 2293, 2297, 2309, 2311, 2323, 2329, 2333, 2339, 2341, 2347, 2351, 2357, 2363, 2369, 2371, 2377, 2381, 2383, 2389, 2393, 2399, 2407, 2411, 2413, 2417, 2419, 2423, 2437, 2441, 2447, 2449, 2459, 2461, 2467, 2473, 2477, 2479, 2489, 2491, 2501, 2503, 2507, 2521, 2531, 2533, 2537, 2539, 2543, 2549, 2551, 2557, 2567, 2573, 2579, 2581, 2591, 2593, 2599, 2603, 2609, 2617, 2621, 2623, 2627, 2633, 2641, 2647, 2657, 2659, 2663, 2669, 2671, 2677, 2683, 2687, 2689, 2693, 2699, 2701, 2707, 2711, 2713, 2719, 2729, 2731, 2741, 2747, 2749, 2753, 2759, 2767, 2771, 2773, 2777, 2789, 2791, 2797, 2801, 2803, 2809, 2813, 2819, 2831, 2833, 2837, 2839, 2843, 2851, 2857, 2861, 2867, 2869, 2879, 2881, 2887, 2897, 2903, 2909, 2911, 2917, 2921, 2923, 2927, 2929, 2939, 2941, 2953, 2957, 2963, 2969, 2971, 2983, 2987, 2993, 2999, 3001, 3007, 3011, 3013, 3019, 3023, 3037, 3041, 3043, 3049, 3053, 3061, 3067, 3071, 3077, 3079, 3083, 3089, 3097, 3103, 3109, 3119, 3121, 3127, 3131, 3137, 3139, 3149, 3151, 3161, 3163, 3167, 3169, 3173, 3181, 3187, 3191, 3193, 3197, 3203, 3209, 3217, 3221, 3229, 3233, 3239, 3247, 3251, 3253, 3257, 3259, 3271, 3277, 3281, 3287, 3293, 3299, 3301, 3307, 3313, 3317, 3319, 3323, 3329, 3331, 3337, 3343, 3347, 3349, 3359, 3361, 3371, 3373, 3379, 3383, 3389, 3391, 3397, 3401, 3403, 3407, 3413, 3427, 3431, 3433, 3439, 3449, 3457, 3461, 3463, 3467, 3469, 3473, 3481, 3491, 3499, 3503, 3511, 3517, 3527, 3529, 3533, 3539, 3541, 3547, 3551, 3557, 3559, 3569, 3571, 3581, 3583, 3587, 3589, 3593, 3599, 3607, 3611, 3613, 3617, 3623, 3629, 3631, 3637, 3643, 3649, 3659, 3667, 3671, 3673, 3677, 3683, 3691, 3697, 3701, 3709, 3713, 3719, 3721, 3727, 3733, 3737, 3739, 3743, 3749, 3761, 3763, 3767, 3769, 3779, 3781, 3791, 3793, 3797, 3799, 3803, 3811, 3821, 3823, 3827, 3833, 3841, 3847, 3851, 3853, 3859, 3863, 3869, 3877, 3881, 3889, 3893, 3901, 3907, 3911, 3917, 3919, 3923, 3929, 3931, 3937, 3943, 3947, 3953, 3959, 3961, 3967, 3973, 3977, 3979, 3989, 4001, 4003, 4007, 4009, 4013, 4019, 4021, 4027, 4031, 4033, 4049, 4051, 4057, 4061, 4063, 4073, 4079, 4087, 4091, 4093, 4097, 4099, 4111, 4117, 4127, 4129, 4133, 4139, 4141, 4153, 4157, 4159, 4163, 4171, 4177, 4181, 4183, 4187, 4189, 4201, 4211, 4217, 4219, 4223, 4229, 4231, 4237, 4241, 4243, 4247, 4253, 4259, 4261, 4267, 4271, 4273, 4283, 4289, 4297, 4307, 4309, 4313, 4321, 4327, 4331, 4337, 4339, 4343, 4349, 4351, 4357, 4363, 4369, 4373, 4379, 4387, 4391, 4393, 4397, 4399, 4409, 4421, 4423, 4427, 4429, 4439, 4441, 4447, 4451, 4453, 4457, 4463, 4469, 4471, 4481, 4483, 4489, 4493, 4507, 4513, 4517, 4519, 4523, 4531, 4541, 4547, 4549, 4553, 4559, 4561, 4567, 4573, 4577, 4579, 4583, 4591, 4597, 4601, 4603, 4607, 4619, 4621, 4633, 4637, 4639, 4643, 4649, 4651, 4657, 4661, 4663, 4673, 4679, 4681, 4687, 4691, 4699, 4703, 4709, 4717, 4721, 4723, 4727, 4729, 4733, 4747, 4751, 4757, 4759, 4769, 4777, 4783, 4787, 4789, 4793, 4799, 4801, 4811, 4813, 4817, 4819, 4831, 4841, 4843, 4847, 4853, 4859, 4861, 4867, 4871, 4877, 4883, 4889, 4891, 4897, 4903, 4909, 4913, 4919, 4931, 4933, 4937, 4943, 4951, 4957, 4967, 4969, 4973, 4981, 4987, 4993, 4997, 4999, 5003, 5009, 5011, 5017, 5021, 5023, 5029, 5039, 5041, 5051, 5053, 5059, 5063, 5069, 5077, 5081, 5087, 5099, 5101, 5107, 5111, 5113, 5119, 5123, 5129, 5141, 5143, 5147, 5149, 5153, 5167, 5171, 5177, 5179, 5183, 5189, 5191, 5197, 5207, 5209, 5219, 5221, 5227, 5231, 5233, 5237, 5249, 5251, 5261, 5263, 5267, 5273, 5279, 5281, 5287, 5293, 5297, 5303, 5309, 5311, 5321, 5323, 5329, 5333, 5339, 5347, 5351, 5353, 5359, 5363, 5371, 5377, 5381, 5387, 5389, 5393, 5399, 5407, 5413, 5417, 5419, 5429, 5431, 5437, 5441, 5443, 5449, 5459, 5461, 5471, 5477, 5479, 5483, 5491, 5497, 5501, 5503, 5507, 5513, 5519, 5521, 5527, 5531, 5539, 5543, 5549, 5557, 5561, 5563, 5567, 5569, 5573, 5581, 5587, 5591, 5597, 5609, 5611, 5617, 5623, 5627, 5633, 5639, 5641, 5647, 5651, 5653, 5657, 5659, 5669, 5671, 5683, 5689, 5693, 5699, 5701, 5711, 5713, 5717, 5723, 5729, 5737, 5741, 5743, 5749, 5767, 5771, 5773, 5777, 5779, 5783, 5791, 5801, 5807, 5809, 5813, 5821, 5827, 5833, 5839, 5843, 5849, 5851, 5857, 5861, 5867, 5869, 5879, 5881, 5891, 5893, 5897, 5899, 5903, 5909, 5911, 5917, 5921, 5923, 5927, 5933, 5939, 5947, 5953, 5959, 5963, 5969, 5977, 5981, 5983, 5987, 5989, 6001, 6007, 6011, 6023, 6029, 6031, 6037, 6043, 6047, 6049, 6053, 6059, 6067, 6073, 6077, 6079, 6089, 6091, 6101, 6103, 6107, 6109, 6113, 6119, 6121, 6131, 6133, 6137, 6143, 6151, 6157, 6161, 6163, 6169, 6173, 6179, 6187, 6191, 6197, 6199, 6203, 6211, 6217, 6221, 6229, 6233, 6239, 6241, 6247, 6257, 6263, 6269, 6271, 6277, 6283, 6287, 6289, 6299, 6301, 6311, 6313, 6317, 6319, 6323, 6329, 6337, 6341, 6343, 6353, 6359, 6361, 6367, 6371, 6373, 6379, 6389, 6397, 6401, 6403, 6407, 6421, 6427, 6431, 6437, 6439, 6443, 6449, 6451, 6463, 6467, 6469, 6473, 6481, 6491, 6493, 6497, 6499, 6509, 6511, 6521, 6527, 6529, 6533, 6541, 6547, 6551, 6553, 6557, 6563, 6569, 6571, 6577, 6581, 6583, 6593, 6599, 6607, 6613, 6619, 6623, 6631, 6637, 6641, 6647, 6649, 6653, 6659, 6661, 6667, 6673, 6679, 6683, 6689, 6691, 6697, 6701, 6703, 6707, 6709, 6719, 6731, 6733, 6737, 6739, 6749, 6751, 6757, 6761, 6763, 6767, 6779, 6781, 6791, 6793, 6803, 6817, 6821, 6823, 6827, 6829, 6833, 6841, 6847, 6857, 6859, 6863, 6869, 6871, 6883, 6887, 6889, 6893, 6899, 6901, 6907, 6911, 6913, 6917, 6931, 6943, 6947, 6949, 6953, 6959, 6961, 6967, 6971, 6973, 6977, 6983, 6989, 6991, 6997, 7001, 7003, 7009, 7013, 7019, 7027, 7031, 7037, 7039, 7043, 7057, 7061, 7067, 7069, 7079, 7081, 7087, 7093, 7097, 7099, 7103, 7109, 7121, 7123, 7127, 7129, 7141, 7151, 7153, 7157, 7159, 7169, 7171, 7177, 7181, 7187, 7193, 7199, 7201, 7207, 7211, 7213, 7219, 7223, 7229, 7237, 7243, 7247, 7253, 7261, 7277, 7279, 7283, 7289, 7291, 7297, 7303, 7307, 7309, 7313, 7321, 7327, 7331, 7333, 7339, 7349, 7351, 7361, 7363, 7367, 7369, 7373, 7379, 7387, 7391, 7393, 7409, 7411, 7417, 7421, 7429, 7433, 7439, 7451, 7453, 7457, 7459, 7463, 7471, 7477, 7481, 7487, 7489, 7493, 7499, 7507, 7517, 7519, 7523, 7529, 7531, 7537, 7541, 7543, 7547, 7549, 7559, 7561, 7571, 7573, 7577, 7583, 7589, 7591, 7597, 7603, 7607, 7613, 7619, 7621, 7627, 7633, 7639, 7643, 7649, 7661, 7663, 7669, 7673, 7681, 7687, 7691, 7697, 7699, 7703, 7717, 7723, 7727, 7729, 7739, 7741, 7747, 7751, 7753, 7757, 7759, 7769, 7771, 7781, 7783, 7789, 7793, 7801, 7807, 7811, 7817, 7823, 7829, 7831, 7837, 7841, 7849, 7853, 7859, 7867, 7871, 7873, 7877, 7879, 7883, 7897, 7901, 7907, 7913, 7919, 7921, 7927, 7933, 7937, 7939, 7949, 7951, 7957, 7961, 7963, 7967, 7979, 7981, 7991, 7993, 7999, 8003, 8009, 8011, 8017, 8023, 8027, 8033, 8039, 8051, 8053, 8059, 8069, 8077, 8081, 8083, 8087, 8089, 8093, 8101, 8111, 8117, 8119, 8123, 8131, 8137, 8143, 8147, 8149, 8153, 8159, 8161, 8167, 8171, 8179, 8189, 8191, 8201, 8207, 8209, 8213, 8219, 8221, 8227, 8231, 8233, 8237, 8243, 8249, 8251, 8257, 8263, 8269, 8273, 8279, 8287, 8291, 8293, 8297, 8299, 8303, 8311, 8317, 8321, 8329, 8339, 8341, 8347, 8353, 8357, 8363, 8369, 8377, 8381, 8383, 8387, 8389, 8399, 8401, 8413, 8417, 8419, 8423, 8429, 8431, 8441, 8443, 8447, 8453, 8461, 8467, 8471, 8473, 8479, 8483, 8497, 8501, 8507, 8509, 8513, 8521, 8527, 8531, 8537, 8539, 8543, 8549, 8551, 8557, 8563, 8573, 8579, 8581, 8587, 8597, 8599, 8609, 8611, 8621, 8623, 8627, 8629, 8633, 8639, 8641, 8647, 8651, 8653, 8663, 8669, 8677, 8681, 8683, 8689, 8693, 8699, 8707, 8711, 8713, 8717, 8719, 8731, 8737, 8741, 8747, 8753, 8759, 8761, 8773, 8777, 8779, 8783, 8791, 8797, 8803, 8807, 8809, 8819, 8821, 8831, 8837, 8839, 8843, 8849, 8851, 8857, 8861, 8863, 8867, 8873, 8881, 8887, 8891, 8893, 8903, 8909, 8917, 8923, 8927, 8929, 8933, 8941, 8947, 8951, 8959, 8963, 8969, 8971, 8977, 8989, 8993, 8999, 9001, 9007, 9011, 9013, 9017, 9019, 9029, 9041, 9043, 9047, 9049, 9059, 9067, 9071, 9073, 9077, 9083, 9089, 9091, 9101, 9103, 9109, 9127, 9131, 9133, 9137, 9143, 9151, 9157, 9161, 9167, 9169, 9173, 9179, 9181, 9187, 9193, 9197, 9199, 9203, 9209, 9211, 9221, 9223, 9227, 9239, 9241, 9253, 9257, 9259, 9263, 9271, 9277, 9281, 9283, 9287, 9293, 9299, 9301, 9307, 9311, 9313, 9319, 9323, 9329, 9337, 9341, 9343, 9349, 9353, 9367, 9371, 9377, 9379, 9389, 9391, 9397, 9403, 9407, 9409, 9413, 9419, 9421, 9431, 9433, 9437, 9439, 9461, 9463, 9467, 9469, 9473, 9479, 9481, 9487, 9491, 9497, 9509, 9511, 9517, 9521, 9523, 9533, 9539, 9547, 9551, 9553, 9557, 9563, 9571, 9577, 9587, 9589, 9593, 9599, 9601, 9613, 9617, 9619, 9623, 9629, 9631, 9637, 9641, 9643, 9649, 9661, 9671, 9673, 9677, 9679, 9683, 9689, 9697, 9701, 9703, 9707, 9719, 9721, 9727, 9731, 9733, 9739, 9743, 9749, 9761, 9767, 9769, 9773, 9781, 9787, 9791, 9797, 9799, 9803, 9809, 9811, 9817, 9827, 9829, 9833, 9839, 9847, 9851, 9853, 9857, 9859, 9869, 9871, 9881, 9883, 9887, 9899, 9901, 9907, 9913, 9917, 9923, 9929, 9931, 9937, 9941, 9943, 9949, 9953, 9959, 9967, 9973, 9979, 9983, 9991, 10001, 10007, 10009, 10013, 10019, 10027, 10033, 10037, 10039, 10051, 10057, 10061, 10063, 10067, 10069, 10079, 10081, 10091, 10093, 10097, 10099, 10103, 10111, 10117, 10121, 10123, 10133, 10139, 10141, 10147, 10151, 10159, 10163, 10169, 10177, 10181, 10183, 10187, 10189, 10193, 10201, 10207, 10211, 10217, 10223, 10229, 10237, 10243, 10247, 10249, 10253, 10259, 10261, 10267, 10271, 10273, 10277, 10279, 10289, 10291, 10301, 10303, 10313, 10319, 10321, 10327, 10331, 10333, 10337, 10343, 10349, 10357, 10363, 10369, 10379, 10391, 10393, 10397, 10399, 10403, 10411, 10421, 10427, 10429, 10433, 10441, 10447, 10453, 10457, 10459, 10463, 10469, 10471, 10477, 10481, 10487, 10489, 10499, 10501, 10511, 10513, 10519, 10523, 10529, 10531, 10537, 10541, 10547, 10553, 10559, 10561, 10567, 10573, 10579, 10583, 10589, 10597, 10601, 10603, 10607, 10609, 10613, 10627, 10631, 10639, 10643, 10649, 10651, 10657, 10663, 10667, 10669, 10679, 10687, 10691, 10693, 10697, 10709, 10711, 10721, 10723, 10727, 10729, 10733, 10739, 10741, 10753, 10757, 10763, 10771, 10781, 10783, 10789, 10793, 10799, 10807, 10811, 10817, 10819, 10823, 10831, 10837, 10841, 10847, 10849, 10853, 10859, 10861, 10867, 10873, 10877, 10883, 10889, 10891, 10897, 10903, 10909, 10919, 10921, 10931, 10937, 10939, 10943, 10949, 10951, 10957, 10961, 10963, 10973, 10979, 10981, 10987, 10991, 10993, 10999, 11003, 11009, 11017, 11021, 11023, 11027, 11029, 11041, 11047, 11051, 11057, 11059, 11069, 11071, 11083, 11087, 11093, 11101, 11107, 11111, 11113, 11117, 11119, 11129, 11131, 11147, 11149, 11153, 11159, 11161, 11171, 11173, 11177, 11183, 11189, 11191, 11197, 11201, 11203, 11213, 11227, 11233, 11237, 11239, 11243, 11251, 11257, 11261, 11267, 11269, 11273, 11279, 11281, 11287, 11293, 11299, 11303, 11309, 11311, 11317, 11321, 11327, 11329, 11339, 11351, 11353, 11357, 11359, 11369, 11371, 11377, 11381, 11383, 11387, 11393, 11399, 11411, 11413, 11419, 11423, 11437, 11441, 11443, 11447, 11449, 11461, 11467, 11471, 11477, 11483, 11489, 11491, 11497, 11503, 11507, 11509, 11513, 11519, 11521, 11527, 11533, 11537, 11549, 11551, 11563, 11567, 11569, 11573, 11579, 11581, 11587, 11591, 11593, 11597, 11603, 11611, 11617, 11621, 11623, 11629, 11633, 11639, 11647, 11651, 11653, 11657, 11659, 11663, 11677, 11681, 11689, 11699, 11701, 11707, 11717, 11719, 11723, 11729, 11731, 11741, 11743, 11747, 11749, 11761, 11771, 11773, 11777, 11779, 11783, 11789, 11797, 11801, 11807, 11813, 11819, 11821, 11827, 11831, 11833, 11839, 11849, 11857, 11861, 11863, 11867, 11873, 11881, 11887, 11897, 11899, 11903, 11909, 11911, 11917, 11923, 11927, 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26099, 26101, 26107, 26111, 26113, 26119, 26123, 26129, 26137, 26141, 26149, 26153, 26161, 26167, 26171, 26177, 26179, 26183, 26189, 26197, 26203, 26207, 26209, 26219, 26227, 26231, 26233, 26237, 26239, 26249, 26251, 26261, 26263, 26267, 26269, 26281, 26287, 26291, 26293, 26297, 26303, 26309, 26311, 26317, 26321, 26329, 26333, 26339, 26347, 26353, 26357, 26359, 26363, 26371, 26381, 26387, 26393, 26399, 26401, 26407, 26413, 26417, 26419, 26423, 26431, 26437, 26441, 26443, 26447, 26449, 26459, 26461, 26471, 26473, 26479, 26483, 26489, 26491, 26497, 26501, 26503, 26513, 26519, 26527, 26531, 26539, 26549, 26557, 26561, 26563, 26567, 26569, 26573, 26581, 26591, 26597, 26599, 26603, 26617, 26623, 26627, 26629, 26633, 26639, 26641, 26647, 26651, 26657, 26659, 26669, 26671, 26681, 26683, 26687, 26693, 26699, 26701, 26707, 26711, 26713, 26717, 26723, 26729, 26731, 26737, 26743, 26749, 26753, 26759, 26771, 26773, 26777, 26779, 26783, 26791, 26797, 26801, 26809, 26813, 26821, 26827, 26833, 26837, 26839, 26843, 26849, 26857, 26861, 26863, 26867, 26869, 26879, 26881, 26891, 26893, 26899, 26903, 26909, 26911, 26921, 26927, 26933, 26941, 26947, 26951, 26953, 26959, 26963, 26969, 26977, 26981, 26987, 26989, 26993, 27007, 27011, 27017, 27019, 27023, 27029, 27031, 27037, 27043, 27047, 27059, 27061, 27067, 27073, 27077, 27089, 27091, 27101, 27103, 27107, 27109, 27113, 27119, 27121, 27127, 27133, 27143, 27149, 27151, 27161, 27163, 27169, 27173, 27179, 27187, 27191, 27193, 27197, 27199, 27211, 27217, 27221, 27227, 27229, 27233, 27239, 27241, 27253, 27257, 27259, 27263, 27271, 27277, 27281, 27283, 27289, 27299, 27301, 27311, 27317, 27319, 27323, 27329, 27331, 27337, 27341, 27343, 27347, 27353, 27359, 27361, 27367, 27371, 27373, 27383, 27389, 27397, 27403, 27407, 27409, 27413, 27421, 27427, 27431, 27437, 27439, 27449, 27451, 27457, 27463, 27473, 27479, 27481, 27487, 27491, 27493, 27497, 27499, 27509, 27523, 27527, 27529, 27539, 27541, 27551, 27553, 27557, 27563, 27569, 27571, 27581, 27583, 27589, 27593, 27607, 27611, 27613, 27617, 27619, 27623, 27631, 27637, 27641, 27647, 27649, 27653, 27659, 27661, 27667, 27673, 27679, 27683, 27689, 27691, 27697, 27701, 27707, 27719, 27721, 27733, 27737, 27739, 27743, 27749, 27751, 27757, 27761, 27763, 27767, 27773, 27779, 27787, 27791, 27793, 27799, 27803, 27809, 27817, 27821, 27823, 27827, 27829, 27847, 27851, 27857, 27869, 27871, 27877, 27883, 27887, 27889, 27893, 27899, 27901, 27913, 27917, 27919, 27931, 27941, 27943, 27947, 27949, 27953, 27959, 27961, 27967, 27971, 27977, 27983, 27991, 27997, 28001, 28003, 28009, 28013, 28019, 28027, 28031, 28033, 28037, 28043, 28051, 28057, 28069, 28073, 28079, 28081, 28087, 28097, 28099, 28103, 28109, 28111, 28117, 28121, 28123, 28129, 28139, 28141, 28151, 28153, 28157, 28159, 28163, 28169, 28177, 28181, 28183, 28187, 28199, 28201, 28207, 28211, 28213, 28219, 28229, 28241, 28243, 28247, 28253, 28261, 28267, 28271, 28277, 28279, 28283, 28289, 28291, 28297, 28307, 28309, 28313, 28319, 28321, 28331, 28333, 28337, 28339, 28349, 28351, 28361, 28363, 28367, 28373, 28381, 28387, 28393, 28397, 28403, 28409, 28411, 28417, 28421, 28423, 28429, 28433, 28439, 28447, 28451, 28453, 28459, 28463, 28471, 28477, 28481, 28487, 28489, 28493, 28499, 28507, 28513, 28517, 28519, 28529, 28531, 28537, 28541, 28543, 28547, 28549, 28559, 28571, 28573, 28577, 28579, 28583, 28591, 28597, 28601, 28603, 28607, 28619, 28621, 28627, 28631, 28643, 28649, 28657, 28661, 28663, 28667, 28669, 28673, 28681, 28687, 28697, 28703, 28709, 28711, 28723, 28727, 28729, 28733, 28739, 28741, 28747, 28751, 28753, 28757, 28759, 28771, 28781, 28783, 28789, 28793, 28799, 28801, 28807, 28811, 28813, 28817, 28823, 28829, 28837, 28841, 28843, 28849, 28859, 28867, 28871, 28877, 28879, 28883, 28891, 28901, 28907, 28909, 28913, 28921, 28927, 28933, 28937, 28939, 28943, 28949, 28957, 28961, 28967, 28969, 28979, 28981, 28991, 28993, 28997, 28999, 29009, 29011, 29017, 29021, 29023, 29027, 29033, 29039, 29041, 29047, 29053, 29059, 29063, 29069, 29077, 29083, 29087, 29089, 29093, 29101, 29111, 29119, 29123, 29129, 29131, 29137, 29143, 29147, 29149, 29153, 29167, 29171, 29173, 29177, 29179, 29189, 29191, 29201, 29203, 29207, 29209, 29213, 29219, 29221, 29231, 29233, 29243, 29251, 29257, 29261, 29269, 29273, 29279, 29287, 29291, 29297, 29299, 29303, 29311, 29317, 29321, 29327, 29329, 29333, 29339, 29347, 29353, 29357, 29363, 29369, 29371, 29377, 29383, 29387, 29389, 29399, 29401, 29411, 29413, 29417, 29423, 29429, 29431, 29437, 29441, 29443, 29453, 29459, 29461, 29467, 29473, 29479, 29483, 29489, 29501, 29503, 29507, 29509, 29521, 29527, 29531, 29537, 29539, 29543, 29551, 29563, 29567, 29569, 29573, 29581, 29587, 29591, 29593, 29597, 29599, 29609, 29611, 29621, 29629, 29633, 29639, 29641, 29647, 29651, 29657, 29663, 29669, 29671, 29677, 29681, 29683, 29693, 29699, 29707, 29713, 29717, 29719, 29723, 29737, 29741, 29747, 29749, 29753, 29759, 29761, 29767, 29773, 29779, 29789, 29791, 29797, 29801, 29803, 29807, 29819, 29831, 29833, 29837, 29839, 29849, 29851, 29857, 29863, 29867, 29873, 29879, 29881, 29891, 29893, 29899, 29903, 29917, 29921, 29923, 29927, 29929, 29933, 29941, 29947, 29951, 29957, 29959, 29963, 29969, 29971, 29977, 29983, 29987, 29989, 29993, 29999, 30001, 30007, 30011, 30013, 30029});

	private static HashSet<Integer> toHashSet(int[] arr) {
		HashSet<Integer> hashset = new HashSet<Integer>(arr.length<<1); // sparse hashset -> less entries per list -> faster lookup!
		for (int i : arr) hashset.add(i);
		return hashset;
	}
	
	//private TDivPrimeTest tdiv = new TDivPrimeTest();
	private MillerRabinTest millerRabinTest = new MillerRabinTest();
	private LucasTest lucasTest = new LucasTest();

    public boolean isProbablePrime(long N) {
    	return isProbablePrime(BigInteger.valueOf(N)); // TODO: faster implementation for long?
    }

    public boolean isProbablePrime(BigInteger N) {
        N = N.abs(); // sign is irrelevant
        if (!N.testBit(0)) return N.equals(I_2); // even N>2 is not prime

        // For small N, trial division is much faster than BPSW
        if (N.bitLength() < 32) {
        	return TDivPrimeTest.getInstance().isPrime(N.intValue());
        }
        
		// Test residues % 30030. Note that N<30030 have been exclude by trial division above.
		if (!primeRestsMod30030.contains(N.mod(BIG_30030).intValue())) return false;

		// The Lucas test is not carried out if N fails the base 2 Miller-Rabin test.
        return millerRabinTest.testSingleBase(N, I_2) && lucasTest.isStrongProbablePrime(N);
    }
    
    /**
     * @param N
     * @return first prime > N
     */
    public BigInteger nextProbablePrime(BigInteger N) {
    	// Java's built-in function using a sieve to identify prime candidates is stronger for N>=256 bit.
    	if (N.bitLength()>=256) return N.nextProbablePrime();
    	
        N = N.abs(); // sign is irrelevant
        if (N.bitLength()<=1) return I_2;
    	// skip argument and make even argument odd
        N = N.testBit(0) ? N.add(I_2) : N.add(I_1);
    	
    	// loop to next prime
    	while (!isProbablePrime(N)) N = N.add(I_2);
    	return N;
    }
}