gap> Factors(3^157-2^157); #I #I Check for n = b^k +/- 1 #I #I Factors already found : [ ] #I #I #I Trial division by all primes p < 1000 #I #I Trial division by some already known primes #I #I Check for perfect powers #I #I Pollard's Rho Steps = 16384, Cluster = 615 Number to be factored : 809164816771822689786320611039172856169453805776863539644272916937931852691 #I Intermediate result : [ [ 24325267 ], [ 332643755471141463642031395190512341003062291475305713867096\ 67644673 ] ] #I #I Factors already found : [ 24325267 ] #I #I #I Pollard's p - 1 Limit1 = 10000, Limit2 = 400000 Number to be factored : 33264375547114146364203139519051234100306229147530571386709667644673 #I p-1 for n = 33264375547114146364203139519051234100306229147530571386709667644673 a : 2, Limit1 : 10000, Limit2 : 400000 #I First stage #I Second stage #I #I Williams' p + 1 Residues = 2, Limit1 = 2000, Limit2 = 80000 Number to be factored : 33264375547114146364203139519051234100306229147530571386709667644673 #I p+1 for n = 33264375547114146364203139519051234100306229147530571386709667644673 Residues : 2, Limit1 : 2000, Limit2 : 80000 #I Residue no. 1 #I First stage #I Second stage #I Residue no. 2 #I First stage #I Second stage #I #I Elliptic Curves Method (ECM) Curves = Init. Limit1 = , Init. Limit2 = , Delta = Number to be factored : 33264375547114146364203139519051234100306229147530571386709667644673 #I ECM for n = 33264375547114146364203139519051234100306229147530571386709667644673 Curves : 123, Initial Limit1 : 200, Initial Limit2 : 20000, Delta : 200 #I Curve no. 1, Limit1 : 200, Limit2 : 20000 #I First stage #I Second stage #I Curve no. 2, Limit1 : 400, Limit2 : 40000 #I First stage #I Second stage #I Curve no. 3, Limit1 : 600, Limit2 : 60000 #I First stage #I Second stage #I Curve no. 4, Limit1 : 800, Limit2 : 80000 #I First stage #I Second stage #I Curve no. 5, Limit1 : 1000, Limit2 : 100000 #I First stage #I Second stage #I Curve no. 6, Limit1 : 1200, Limit2 : 120000 #I First stage #I Second stage #I Curve no. 7, Limit1 : 1400, Limit2 : 140000 #I First stage #I Second stage #I Curve no. 8, Limit1 : 1600, Limit2 : 160000 #I First stage #I Second stage #I Curve no. 9, Limit1 : 1800, Limit2 : 180000 #I First stage #I Second stage #I Curve no. 10, Limit1 : 2000, Limit2 : 200000 #I First stage #I Second stage #I Curve no. 11, Limit1 : 2200, Limit2 : 220000 #I First stage #I Second stage #I Curve no. 12, Limit1 : 2400, Limit2 : 240000 #I First stage #I Second stage #I Curve no. 13, Limit1 : 2600, Limit2 : 260000 #I First stage #I Second stage #I Curve no. 14, Limit1 : 2800, Limit2 : 280000 #I First stage #I Second stage #I Curve no. 15, Limit1 : 3000, Limit2 : 300000 #I First stage #I Second stage #I Curve no. 16, Limit1 : 3200, Limit2 : 320000 #I First stage #I Second stage #I Curve no. 17, Limit1 : 3400, Limit2 : 340000 #I First stage #I Second stage #I Curve no. 18, Limit1 : 3600, Limit2 : 360000 #I First stage #I Second stage #I Curve no. 19, Limit1 : 3800, Limit2 : 380000 #I First stage #I Second stage #I Curve no. 20, Limit1 : 4000, Limit2 : 400000 #I First stage #I Second stage #I Curve no. 21, Limit1 : 4200, Limit2 : 420000 #I First stage #I Second stage #I Curve no. 22, Limit1 : 4400, Limit2 : 440000 #I First stage #I Second stage #I Curve no. 23, Limit1 : 4600, Limit2 : 460000 #I First stage #I Second stage #I Curve no. 24, Limit1 : 4800, Limit2 : 480000 #I First stage #I Second stage #I Curve no. 25, Limit1 : 5000, Limit2 : 500000 #I First stage #I Second stage #I Curve no. 26, Limit1 : 5200, Limit2 : 520000 #I First stage #I Second stage #I Curve no. 27, Limit1 : 5400, Limit2 : 540000 #I First stage #I Second stage #I Curve no. 28, Limit1 : 5600, Limit2 : 560000 #I First stage #I Second stage #I Curve no. 29, Limit1 : 5800, Limit2 : 580000 #I First stage #I Second stage #I Curve no. 30, Limit1 : 6000, Limit2 : 600000 #I First stage #I Second stage #I Curve no. 31, Limit1 : 6200, Limit2 : 620000 #I First stage #I Second stage #I Curve no. 32, Limit1 : 6400, Limit2 : 640000 #I First stage #I Second stage #I Curve no. 33, Limit1 : 6600, Limit2 : 660000 #I First stage #I Second stage #I Curve no. 34, Limit1 : 6800, Limit2 : 680000 #I First stage #I Second stage #I Curve no. 35, Limit1 : 7000, Limit2 : 700000 #I First stage #I Second stage #I Curve no. 36, Limit1 : 7200, Limit2 : 720000 #I First stage #I Second stage #I Curve no. 37, Limit1 : 7400, Limit2 : 740000 #I First stage #I Second stage #I Curve no. 38, Limit1 : 7600, Limit2 : 760000 #I First stage #I Second stage #I Curve no. 39, Limit1 : 7800, Limit2 : 780000 #I First stage #I Second stage #I Curve no. 40, Limit1 : 8000, Limit2 : 800000 #I First stage #I Second stage #I Curve no. 41, Limit1 : 8200, Limit2 : 820000 #I First stage #I Second stage #I Curve no. 42, Limit1 : 8400, Limit2 : 840000 #I First stage #I Second stage #I Curve no. 43, Limit1 : 8600, Limit2 : 860000 #I First stage #I Second stage #I Curve no. 44, Limit1 : 8800, Limit2 : 880000 #I First stage #I Second stage #I Curve no. 45, Limit1 : 9000, Limit2 : 900000 #I First stage #I Second stage #I Curve no. 46, Limit1 : 9200, Limit2 : 920000 #I First stage #I Second stage #I Curve no. 47, Limit1 : 9400, Limit2 : 940000 #I First stage #I Second stage #I Curve no. 48, Limit1 : 9600, Limit2 : 960000 #I First stage #I Second stage #I Curve no. 49, Limit1 : 9800, Limit2 : 980000 #I First stage #I Second stage #I Curve no. 50, Limit1 : 10000, Limit2 : 1000000 #I First stage #I Second stage #I Curve no. 51, Limit1 : 10200, Limit2 : 1020000 #I First stage #I Second stage #I Curve no. 52, Limit1 : 10400, Limit2 : 1040000 #I First stage #I Second stage #I Curve no. 53, Limit1 : 10600, Limit2 : 1060000 #I First stage #I Second stage #I Curve no. 54, Limit1 : 10800, Limit2 : 1080000 #I First stage #I Second stage #I Curve no. 55, Limit1 : 11000, Limit2 : 1100000 #I First stage #I Second stage #I Curve no. 56, Limit1 : 11200, Limit2 : 1120000 #I First stage #I Second stage #I Curve no. 57, Limit1 : 11400, Limit2 : 1140000 #I First stage #I Second stage #I Curve no. 58, Limit1 : 11600, Limit2 : 1160000 #I First stage #I Second stage #I Curve no. 59, Limit1 : 11800, Limit2 : 1180000 #I First stage #I Second stage #I Curve no. 60, Limit1 : 12000, Limit2 : 1200000 #I First stage #I Second stage #I Curve no. 61, Limit1 : 12200, Limit2 : 1220000 #I First stage #I Second stage #I Curve no. 62, Limit1 : 12400, Limit2 : 1240000 #I First stage #I Second stage #I Curve no. 63, Limit1 : 12600, Limit2 : 1260000 #I First stage #I Second stage #I Curve no. 64, Limit1 : 12800, Limit2 : 1280000 #I First stage #I Second stage #I Curve no. 65, Limit1 : 13000, Limit2 : 1300000 #I First stage #I Second stage #I Curve no. 66, Limit1 : 13200, Limit2 : 1320000 #I First stage #I Second stage #I Curve no. 67, Limit1 : 13400, Limit2 : 1340000 #I First stage #I Second stage #I Curve no. 68, Limit1 : 13600, Limit2 : 1360000 #I First stage #I Second stage #I Curve no. 69, Limit1 : 13800, Limit2 : 1380000 #I First stage #I Second stage #I Curve no. 70, Limit1 : 14000, Limit2 : 1400000 #I First stage #I Second stage #I Curve no. 71, Limit1 : 14200, Limit2 : 1420000 #I First stage #I Second stage #I Curve no. 72, Limit1 : 14400, Limit2 : 1440000 #I First stage #I Second stage #I Curve no. 73, Limit1 : 14600, Limit2 : 1460000 #I First stage #I Second stage #I Curve no. 74, Limit1 : 14800, Limit2 : 1480000 #I First stage #I Second stage #I Curve no. 75, Limit1 : 15000, Limit2 : 1500000 #I First stage #I Second stage #I Curve no. 76, Limit1 : 15200, Limit2 : 1520000 #I First stage #I Second stage #I Curve no. 77, Limit1 : 15400, Limit2 : 1540000 #I First stage #I Second stage #I Curve no. 78, Limit1 : 15600, Limit2 : 1560000 #I First stage #I Second stage #I Curve no. 79, Limit1 : 15800, Limit2 : 1580000 #I First stage #I Second stage #I Curve no. 80, Limit1 : 16000, Limit2 : 1600000 #I First stage #I Second stage #I Curve no. 81, Limit1 : 16200, Limit2 : 1620000 #I First stage #I Second stage #I Curve no. 82, Limit1 : 16400, Limit2 : 1640000 #I First stage #I Second stage #I Curve no. 83, Limit1 : 16600, Limit2 : 1660000 #I First stage #I Second stage #I Curve no. 84, Limit1 : 16800, Limit2 : 1680000 #I First stage #I Second stage #I Curve no. 85, Limit1 : 17000, Limit2 : 1700000 #I First stage #I Second stage #I Curve no. 86, Limit1 : 17200, Limit2 : 1720000 #I First stage #I Second stage #I Curve no. 87, Limit1 : 17400, Limit2 : 1740000 #I First stage #I Second stage #I Curve no. 88, Limit1 : 17600, Limit2 : 1760000 #I First stage #I Second stage #I Curve no. 89, Limit1 : 17800, Limit2 : 1780000 #I First stage #I Second stage #I Curve no. 90, Limit1 : 18000, Limit2 : 1800000 #I First stage #I Second stage #I Curve no. 91, Limit1 : 18200, Limit2 : 1820000 #I First stage #I Second stage #I Curve no. 92, Limit1 : 18400, Limit2 : 1840000 #I First stage #I Second stage #I Curve no. 93, Limit1 : 18600, Limit2 : 1860000 #I First stage #I Second stage #I Curve no. 94, Limit1 : 18800, Limit2 : 1880000 #I First stage #I Second stage #I Curve no. 95, Limit1 : 19000, Limit2 : 1900000 #I First stage #I Second stage #I Curve no. 96, Limit1 : 19200, Limit2 : 1920000 #I First stage #I Second stage #I Curve no. 97, Limit1 : 19400, Limit2 : 1940000 #I First stage #I Second stage #I Curve no. 98, Limit1 : 19600, Limit2 : 1960000 #I First stage #I Second stage #I Curve no. 99, Limit1 : 19800, Limit2 : 1980000 #I First stage #I Second stage #I Curve no. 100, Limit1 : 20000, Limit2 : 2000000 #I First stage #I Second stage #I Curve no. 101, Limit1 : 20200, Limit2 : 2020000 #I Initializing prime differences list, PrimeDiffLimit = 4000000 #I First stage #I Second stage #I Curve no. 102, Limit1 : 20400, Limit2 : 2040000 #I First stage #I Second stage #I Curve no. 103, Limit1 : 20600, Limit2 : 2060000 #I First stage #I Second stage #I Curve no. 104, Limit1 : 20800, Limit2 : 2080000 #I First stage #I Second stage #I Curve no. 105, Limit1 : 21000, Limit2 : 2100000 #I First stage #I Second stage #I Curve no. 106, Limit1 : 21200, Limit2 : 2120000 #I First stage #I Second stage #I Curve no. 107, Limit1 : 21400, Limit2 : 2140000 #I First stage #I Second stage #I Curve no. 108, Limit1 : 21600, Limit2 : 2160000 #I First stage #I Second stage #I Curve no. 109, Limit1 : 21800, Limit2 : 2180000 #I First stage #I Second stage #I Curve no. 110, Limit1 : 22000, Limit2 : 2200000 #I First stage #I Second stage #I Curve no. 111, Limit1 : 22200, Limit2 : 2220000 #I First stage #I Second stage #I Curve no. 112, Limit1 : 22400, Limit2 : 2240000 #I First stage #I Second stage #I Curve no. 113, Limit1 : 22600, Limit2 : 2260000 #I First stage #I Second stage #I Curve no. 114, Limit1 : 22800, Limit2 : 2280000 #I First stage #I Second stage #I Curve no. 115, Limit1 : 23000, Limit2 : 2300000 #I First stage #I Second stage #I Curve no. 116, Limit1 : 23200, Limit2 : 2320000 #I First stage #I Second stage #I Curve no. 117, Limit1 : 23400, Limit2 : 2340000 #I First stage #I Second stage #I Curve no. 118, Limit1 : 23600, Limit2 : 2360000 #I First stage #I Second stage #I Curve no. 119, Limit1 : 23800, Limit2 : 2380000 #I First stage #I Second stage #I Curve no. 120, Limit1 : 24000, Limit2 : 2400000 #I First stage #I Second stage #I Curve no. 121, Limit1 : 24200, Limit2 : 2420000 #I First stage #I Second stage #I Curve no. 122, Limit1 : 24400, Limit2 : 2440000 #I First stage #I Second stage #I Curve no. 123, Limit1 : 24600, Limit2 : 2460000 #I First stage #I Second stage #I #I Multiple Polynomial Quadratic Sieve (MPQS) Number to be factored : 33264375547114146364203139519051234100306229147530571386709667644673 #I Pass no. 1 #I MPQS for n = 33264375547114146364203139519051234100306229147530571386709667644673 #I Digits : 68 #I Multiplier : 1 #I Size of factor base : 3144 #I Factor base : [ -1, 2, 3, 7, 11, 19, 23, 37, 41, 43, 47, 53, 67, 83, 97, 107, 109, 131, 139, 151, 157, 173, 181, 191, 193, 211, 223, 227, 229, 233, 241, 251, 257, 269, 311, 331, 347, 349, 353, 359, 367, 373, 401, 419, 431, 433, 487, 491, 499, 503, 509, 521, 523, 541, 569, 571, 577, 587, 599, 601, 607, 617, 641, 647, 653, 661, 683, 691, 701, 751, 757, 769, 773, 827, 829, 839, 859, 877, 883, 887, 907, 919, 929, 947, 971, 977, 997, 1009, 1013, 1019, 1021, 1039, 1061, 1091, 1103, 1117, 1171, 1181, 1187, 1193, 1217, 1229, 1231, 1277, 1283, 1291, 1297, 1301, 1321, 1381, 1399, 1433, 1459, 1471, 1481, 1483, 1489, 1511, 1531, 1543, 1559, 1567, 1583, 1607, 1613, 1619, 1657, 1663, 1669, 1693, 1697, 1699, 1709, 1721, 1723, 1733, 1741, 1753, 1777, 1783, 1811, 1823, 1861, 1867, 1873, 1877, 1889, 1901, 1913, 1949, 1979, 1987, 1993, 1999, 2003, 2011, 2027, 2039, 2063, 2069, 2081, 2099, 2111, 2113, 2129, 2131, 2141, 2213, 2237, 2239, 2267, 2273, 2287, 2293, 2297, 2311, 2339, 2351, 2381, 2383, 2393, 2411, 2459, 2473, 2477, 2503, 2531, 2539, 2551, 2557, 2579, 2609, 2617, 2621, 2647, 2657, 2659, 2663, 2677, 2683, 2693, 2711, 2719, 2731, 2753, 2767, 2777, 2803, 2833, 2843, 2857, 2861, 2903, 2917, 2953, 2963, 2969, 2971, 3011, 3041, 3049, 3061, 3119, 3169, 3181, 3187, 3203, 3209, 3221, 3229, 3259, 3271, 3301, 3313, 3329, 3331, 3359, 3371, 3389, 3457, 3467, 3517, 3527, 3529, 3541, 3559, 3571, 3581, 3583, 3617, 3631, 3673, 3677, 3697, 3701, 3719, 3727, 3761, 3769, 3797, 3821, 3833, 3847, 3851, 3877, 3881, 3907, 3911, 3917, 3919, 3923, 3929, 3931, 3947, 3989, 4001, 4007, 4019, 4049, 4079, 4091, 4099, 4111, 4217, 4219, 4229, 4231, 4243, 4271, 4289, 4327, 4337, 4339, 4357, 4363, 4373, 4423, 4457, 4481, 4483, 4493, 4507, 4517, 4519, 4523, 4561, 4567, 4583, 4591, 4603, 4621, 4639, 4643, 4657, 4673, 4721, 4723, 4751, 4783, 4787, 4793, 4799, 4801, 4813, 4871, 4877, 4919, 4931, 4969, 4993, 4999, 5003, 5009, 5011, 5023, 5039, 5087, 5113, 5119, 5153, 5171, 5179, 5197, 5261, 5273, 5281, 5297, 5303, 5323, 5333, 5351, 5387, 5399, 5407, 5417, 5419, 5431, 5441, 5471, 5479, 5503, 5507, 5519, 5521, 5557, 5563, 5623, 5647, 5653, 5657, 5659, 5683, 5689, 5701, 5711, 5737, 5791, 5807, 5813, 5827, 5843, 5851, 5861, 5867, 5869, 5881, 5897, 5903, 5927, 5953, 5981, 5987, 6011, 6037, 6043, 6047, 6053, 6091, 6133, 6143, 6163, 6173, 6197, 6199, 6203, 6221, 6229, 6247, 6257, 6277, 6287, 6299, 6323, 6343, 6359, 6373, 6379, 6389, 6421, 6427, 6451, 6481, 6529, 6569, 6581, 6599, 6607, 6619, 6637, 6653, 6661, 6701, 6703, 6733, 6761, 6763, 6781, 6793, 6803, 6829, 6841, 6869, 6871, 6899, 6911, 6917, 6947, 6961, 6991, 7013, 7039, 7057, 7121, 7127, 7159, 7187, 7207, 7211, 7219, 7229, 7243, 7253, 7309, 7333, 7349, 7351, 7477, 7507, 7517, 7523, 7529, 7541, 7547, 7559, 7603, 7607, 7621, 7639, 7649, 7669, 7687, 7717, 7723, 7727, 7741, 7757, 7789, 7823, 7867, 7873, 7883, 7901, 7907, 7919, 7927, 7937, 7951, 7963, 8039, 8053, 8059, 8081, 8093, 8111, 8161, 8179, 8191, 8209, 8219, 8221, 8231, 8233, 8263, 8273, 8287, 8291, 8297, 8353, 8363, 8377, 8387, 8389, 8423, 8431, 8443, 8513, 8521, 8527, 8537, 8543, 8563, 8597, 8599, 8609, 8663, 8669, 8681, 8693, 8699, 8713, 8719, 8741, 8747, 8779, 8803, 8819, 8831, 8863, 8867, 8923, 8929, 8951, 8963, 8969, 9007, 9011, 9043, 9049, 9091, 9127, 9137, 9151, 9157, 9161, 9181, 9203, 9209, 9221, 9277, 9283, 9337, 9349, 9371, 9377, 9419, 9431, 9463, 9473, 9479, 9491, 9497, 9521, 9533, 9631, 9649, 9697, 9719, 9733, 9739, 9767, 9769, 9787, 9811, 9817, 9829, 9833, 9871, 9887, 9907, 9923, 9941, 9967, 10009, 10037, 10039, 10067, 10091, 10099, 10103, 10111, 10141, 10151, 10163, 10169, 10193, 10211, 10223, 10267, 10289, 10303, 10313, 10331, 10337, 10369, 10399, 10427, 10429, 10457, 10463, 10477, 10487, 10499, 10501, 10529, 10567, 10601, 10613, 10627, 10663, 10667, 10687, 10709, 10711, 10739, 10753, 10771, 10799, 10859, 10867, 10889, 10891, 10903, 10937, 10939, 10949, 10979, 10993, 11003, 11027, 11047, 11069, 11083, 11087, 11131, 11159, 11177, 11197, 11213, 11243, 11279, 11317, 11329, 11351, 11369, 11393, 11423, 11437, 11447, 11467, 11489, 11491, 11497, 11549, 11551, 11579, 11593, 11617, 11621, 11657, 11681, 11699, 11701, 11731, 11801, 11813, 11827, 11833, 11839, 11887, 11897, 11903, 11909, 11927, 11933, 11939, 11941, 11953, 11969, 11981, 11987, 12043, 12073, 12101, 12107, 12109, 12113, 12119, 12143, 12203, 12211, 12239, 12253, 12277, 12301, 12329, 12347, 12373, 12391, 12413, 12421, 12433, 12451, 12473, 12487, 12497, 12503, 12527, 12539, 12547, 12553, 12577, 12583, 12589, 12611, 12619, 12637, 12641, 12647, 12689, 12703, 12713, 12739, 12743, 12757, 12763, 12791, 12799, 12829, 12853, 12889, 12893, 12899, 12907, 12917, 12923, 12941, 12953, 12973, 12979, 13007, 13037, 13049, 13063, 13093, 13099, 13103, 13121, 13127, 13147, 13159, 13177, 13219, 13249, 13259, 13291, 13327, 13337, 13367, 13397, 13411, 13417, 13421, 13553, 13577, 13597, 13619, 13627, 13633, 13649, 13679, 13681, 13687, 13697, 13709, 13711, 13723, 13729, 13751, 13759, 13789, 13807, 13831, 13877, 13879, 13883, 13913, 13921, 13931, 13967, 13997, 13999, 14029, 14051, 14057, 14071, 14087, 14107, 14153, 14159, 14173, 14197, 14207, 14221, 14243, 14249, 14281, 14303, 14321, 14323, 14347, 14387, 14407, 14411, 14419, 14437, 14461, 14489, 14533, 14551, 14557, 14561, 14563, 14591, 14627, 14629, 14633, 14657, 14713, 14717, 14731, 14737, 14747, 14813, 14821, 14843, 14887, 14891, 14923, 14947, 14957, 14969, 14983, 15013, 15017, 15053, 15077, 15131, 15137, 15139, 15173, 15217, 15227, 15233, 15259, 15269, 15313, 15331, 15383, 15427, 15443, 15461, 15467, 15493, 15497, 15511, 15559, 15581, 15601, 15607, 15629, 15641, 15643, 15649, 15667, 15727, 15733, 15749, 15767, 15773, 15797, 15817, 15823, 15877, 15887, 15889, 15937, 15973, 16057, 16061, 16063, 16067, 16069, 16073, 16103, 16139, 16183, 16187, 16193, 16217, 16231, 16267, 16273, 16301, 16319, 16333, 16349, 16361, 16363, 16381, 16417, 16421, 16427, 16433, 16447, 16453, 16477, 16481, 16487, 16519, 16553, 16561, 16567, 16603, 16649, 16661, 16673, 16691, 16699, 16703, 16741, 16747, 16759, 16763, 16787, 16811, 16843, 16871, 16883, 16889, 16931, 16943, 16963, 16979, 16981, 16987, 17011, 17027, 17033, 17053, 17077, 17093, 17099, 17107, 17183, 17189, 17191, 17203, 17209, 17231, 17239, 17257, 17293, 17299, 17327, 17341, 17359, 17377, 17383, 17387, 17431, 17443, 17509, 17519, 17539, 17551, 17573, 17609, 17669, 17729, 17747, 17749, 17827, 17837, 17839, 17881, 17903, 17921, 17957, 17971, 17977, 17987, 17989, 18047, 18089, 18097, 18143, 18181, 18191, 18211, 18217, 18233, 18253, 18269, 18287, 18289, 18301, 18307, 18353, 18397, 18401, 18433, 18439, 18443, 18461, 18481, 18503, 18517, 18521, 18541, 18553, 18583, 18593, 18617, 18671, 18691, 18713, 18719, 18757, 18773, 18793, 18797, 18803, 18899, 18917, 18947, 18959, 18979, 19013, 19051, 19069, 19121, 19141, 19157, 19181, 19207, 19213, 19219, 19231, 19267, 19301, 19309, 19319, 19379, 19387, 19403, 19423, 19433, 19441, 19447, 19469, 19477, 19489, 19501, 19507, 19543, 19553, 19559, 19577, 19597, 19681, 19687, 19751, 19753, 19801, 19813, 19841, 19853, 19891, 19913, 19919, 19937, 19949, 19991, 19997, 20023, 20029, 20047, 20071, 20089, 20107, 20123, 20143, 20149, 20173, 20177, 20183, 20219, 20261, 20269, 20323, 20333, 20341, 20347, 20353, 20357, 20359, 20369, 20399, 20431, 20441, 20477, 20483, 20507, 20509, 20533, 20543, 20551, 20563, 20593, 20639, 20641, 20663, 20693, 20747, 20771, 20773, 20857, 20879, 20899, 20921, 20947, 20963, 20983, 21001, 21011, 21013, 21017, 21019, 21023, 21059, 21061, 21089, 21101, 21149, 21163, 21169, 21191, 21193, 21221, 21227, 21247, 21269, 21277, 21313, 21317, 21341, 21347, 21379, 21407, 21433, 21467, 21481, 21487, 21503, 21523, 21529, 21557, 21559, 21563, 21577, 21589, 21601, 21613, 21647, 21649, 21701, 21713, 21727, 21737, 21751, 21767, 21871, 21929, 21943, 21977, 21991, 22027, 22051, 22073, 22091, 22093, 22123, 22159, 22189, 22193, 22259, 22273, 22283, 22291, 22349, 22367, 22381, 22391, 22397, 22433, 22469, 22481, 22483, 22511, 22543, 22549, 22567, 22619, 22621, 22637, 22691, 22697, 22717, 22721, 22727, 22739, 22777, 22783, 22817, 22859, 22871, 22877, 22901, 22921, 22937, 22961, 22973, 22993, 23003, 23029, 23041, 23053, 23063, 23117, 23143, 23189, 23209, 23251, 23293, 23297, 23311, 23327, 23333, 23369, 23417, 23459, 23497, 23509, 23537, 23557, 23561, 23593, 23599, 23603, 23609, 23623, 23629, 23633, 23663, 23747, 23753, 23761, 23773, 23801, 23813, 23827, 23831, 23833, 23857, 23879, 23887, 23893, 23899, 23911, 23929, 23971, 23977, 24001, 24007, 24019, 24043, 24049, 24061, 24071, 24107, 24121, 24133, 24137, 24169, 24179, 24197, 24229, 24239, 24247, 24317, 24359, 24373, 24407, 24419, 24439, 24443, 24469, 24481, 24499, 24509, 24517, 24527, 24533, 24551, 24571, 24593, 24611, 24623, 24631, 24659, 24671, 24683, 24691, 24697, 24709, 24733, 24781, 24799, 24821, 24841, 24851, 24859, 24889, 24917, 24923, 24943, 25073, 25087, 25097, 25111, 25147, 25169, 25171, 25189, 25247, 25301, 25303, 25307, 25321, 25339, 25373, 25391, 25409, 25411, 25423, 25439, 25447, 25453, 25457, 25541, 25579, 25583, 25589, 25601, 25609, 25621, 25639, 25667, 25673, 25679, 25733, 25741, 25771, 25793, 25799, 25801, 25841, 25867, 25873, 25919, 25933, 25939, 25943, 25951, 25997, 25999, 26003, 26021, 26029, 26111, 26119, 26141, 26153, 26171, 26177, 26183, 26189, 26237, 26249, 26261, 26267, 26293, 26297, 26317, 26339, 26347, 26371, 26399, 26417, 26437, 26449, 26479, 26501, 26513, 26539, 26561, 26573, 26591, 26641, 26681, 26693, 26711, 26713, 26717, 26731, 26759, 26783, 26801, 26821, 26833, 26849, 26861, 26947, 27011, 27031, 27059, 27061, 27073, 27077, 27107, 27179, 27191, 27211, 27241, 27271, 27277, 27361, 27397, 27407, 27427, 27431, 27437, 27449, 27457, 27481, 27509, 27527, 27529, 27539, 27551, 27581, 27583, 27611, 27617, 27631, 27653, 27673, 27689, 27697, 27701, 27733, 27743, 27751, 27779, 27791, 27817, 27847, 27883, 27919, 27941, 27943, 27953, 27961, 27967, 28031, 28051, 28057, 28069, 28081, 28099, 28109, 28111, 28123, 28151, 28163, 28181, 28183, 28201, 28219, 28279, 28289, 28309, 28319, 28349, 28439, 28447, 28477, 28499, 28547, 28559, 28573, 28603, 28619, 28643, 28649, 28657, 28729, 28751, 28807, 28813, 28859, 28871, 28901, 28909, 28921, 28933, 28961, 29009, 29021, 29023, 29033, 29123, 29131, 29147, 29201, 29209, 29221, 29251, 29269, 29287, 29297, 29303, 29311, 29327, 29333, 29347, 29383, 29443, 29527, 29569, 29573, 29599, 29611, 29629, 29633, 29663, 29669, 29671, 29683, 29717, 29741, 29753, 29759, 29789, 29803, 29851, 29863, 29873, 29881, 29917, 29921, 29927, 29983, 29989, 30013, 30029, 30047, 30059, 30103, 30113, 30119, 30139, 30161, 30169, 30181, 30187, 30197, 30203, 30211, 30223, 30241, 30253, 30259, 30293, 30307, 30341, 30347, 30367, 30389, 30391, 30403, 30427, 30449, 30467, 30491, 30497, 30509, 30517, 30539, 30553, 30557, 30559, 30593, 30631, 30643, 30671, 30697, 30757, 30773, 30829, 30839, 30841, 30859, 30871, 30881, 30893, 30911, 30931, 30937, 30941, 30949, 30971, 30983, 31013, 31033, 31051, 31069, 31079, 31139, 31151, 31183, 31189, 31193, 31219, 31223, 31247, 31249, 31259, 31271, 31327, 31337, 31357, 31379, 31391, 31397, 31477, 31481, 31511, 31517, 31573, 31583, 31607, 31627, 31649, 31667, 31699, 31723, 31727, 31729, 31741, 31769, 31771, 31847, 31849, 31859, 31957, 31963, 31973, 31981, 32003, 32057, 32059, 32089, 32117, 32119, 32141, 32143, 32159, 32173, 32213, 32251, 32257, 32261, 32327, 32369, 32377, 32411, 32443, 32467, 32479, 32491, 32497, 32533, 32537, 32561, 32569, 32587, 32687, 32693, 32707, 32713, 32717, 32719, 32771, 32779, 32801, 32803, 32831, 32839, 32887, 32911, 32917, 32933, 32941, 33013, 33029, 33053, 33071, 33073, 33083, 33091, 33179, 33181, 33191, 33203, 33287, 33311, 33343, 33353, 33377, 33391, 33403, 33409, 33457, 33461, 33469, 33503, 33521, 33529, 33563, 33577, 33587, 33599, 33601, 33637, 33647, 33767, 33811, 33827, 33829, 33851, 33857, 33863, 33937, 33941, 33961, 33997, 34031, 34033, 34061, 34141, 34147, 34157, 34183, 34211, 34213, 34217, 34253, 34259, 34261, 34267, 34273, 34283, 34297, 34303, 34319, 34327, 34361, 34381, 34421, 34429, 34439, 34469, 34471, 34483, 34499, 34511, 34537, 34589, 34603, 34649, 34651, 34667, 34693, 34739, 34747, 34763, 34781, 34843, 34849, 34883, 34913, 35051, 35059, 35081, 35083, 35089, 35099, 35117, 35129, 35141, 35149, 35159, 35171, 35201, 35251, 35267, 35327, 35393, 35419, 35423, 35447, 35491, 35509, 35537, 35543, 35569, 35573, 35591, 35593, 35671, 35731, 35759, 35771, 35797, 35801, 35803, 35809, 35837, 35851, 35869, 35879, 35897, 35923, 35951, 35969, 35977, 35983, 35993, 36007, 36013, 36067, 36097, 36107, 36131, 36151, 36161, 36187, 36209, 36217, 36229, 36241, 36269, 36293, 36319, 36343, 36373, 36383, 36433, 36473, 36497, 36529, 36571, 36587, 36607, 36629, 36637, 36653, 36671, 36683, 36691, 36697, 36739, 36749, 36761, 36779, 36781, 36791, 36793, 36809, 36821, 36847, 36899, 36901, 36923, 36931, 36973, 37039, 37061, 37087, 37097, 37117, 37123, 37139, 37159, 37171, 37181, 37223, 37243, 37277, 37309, 37337, 37339, 37363, 37423, 37483, 37489, 37501, 37507, 37511, 37537, 37547, 37549, 37567, 37589, 37607, 37633, 37699, 37717, 37747, 37781, 37783, 37813, 37847, 37853, 37871, 37889, 37897, 37907, 37957, 37963, 37967, 37993, 37997, 38047, 38053, 38069, 38113, 38119, 38177, 38197, 38219, 38231, 38237, 38239, 38261, 38273, 38287, 38299, 38303, 38327, 38393, 38447, 38453, 38459, 38501, 38557, 38561, 38611, 38677, 38713, 38723, 38737, 38783, 38791, 38833, 38839, 38851, 38867, 38891, 38921, 38959, 38977, 39041, 39043, 39119, 39133, 39139, 39163, 39181, 39233, 39239, 39301, 39317, 39341, 39359, 39371, 39373, 39397, 39439, 39451, 39461, 39511, 39541, 39551, 39631, 39659, 39667, 39671, 39679, 39709, 39719, 39733, 39749, 39769, 39799, 39821, 39827, 39829, 39839, 39847, 39857, 39863, 39869, 39929, 39937, 39983, 40009, 40013, 40031, 40063, 40093, 40099, 40123, 40127, 40129, 40151, 40169, 40177, 40189, 40213, 40231, 40357, 40423, 40429, 40433, 40487, 40493, 40507, 40543, 40559, 40591, 40597, 40609, 40627, 40637, 40693, 40697, 40699, 40709, 40739, 40751, 40759, 40763, 40771, 40823, 40829, 40847, 40849, 40867, 40927, 40933, 40949, 40961, 41017, 41039, 41047, 41051, 41057, 41081, 41113, 41117, 41131, 41149, 41179, 41189, 41201, 41221, 41233, 41269, 41299, 41341, 41351, 41357, 41381, 41387, 41389, 41479, 41491, 41507, 41513, 41519, 41539, 41543, 41549, 41593, 41609, 41611, 41621, 41641, 41651, 41659, 41681, 41719, 41737, 41759, 41771, 41843, 41849, 41851, 41863, 41879, 41887, 41893, 41911, 41927, 41953, 41957, 41983, 42013, 42043, 42071, 42073, 42083, 42101, 42131, 42139, 42169, 42193, 42197, 42223, 42227, 42293, 42323, 42337, 42349, 42373, 42379, 42397, 42403, 42407, 42433, 42437, 42443, 42451, 42457, 42461, 42467, 42491, 42509, 42577, 42611, 42641, 42643, 42649, 42677, 42689, 42703, 42709, 42743, 42751, 42767, 42773, 42797, 42829, 42839, 42841, 42853, 42859, 42863, 42901, 42923, 42937, 42943, 42953, 42961, 42979, 43003, 43037, 43049, 43063, 43067, 43133, 43151, 43177, 43189, 43207, 43261, 43271, 43283, 43291, 43313, 43391, 43403, 43411, 43499, 43517, 43543, 43577, 43579, 43607, 43609, 43613, 43627, 43633, 43649, 43661, 43691, 43759, 43787, 43793, 43853, 43913, 43943, 43951, 43987, 43997, 44027, 44041, 44053, 44087, 44089, 44101, 44111, 44119, 44129, 44189, 44201, 44207, 44249, 44257, 44263, 44267, 44269, 44279, 44351, 44357, 44417, 44483, 44491, 44507, 44519, 44533, 44537, 44543, 44549, 44579, 44617, 44633, 44641, 44647, 44683, 44701, 44741, 44771, 44777, 44797, 44809, 44819, 44839, 44843, 44851, 44867, 44893, 44909, 44917, 44939, 44953, 44959, 44963, 44983, 44987, 45013, 45077, 45119, 45121, 45131, 45139, 45161, 45179, 45181, 45191, 45197, 45233, 45247, 45259, 45281, 45329, 45337, 45343, 45413, 45427, 45433, 45481, 45491, 45553, 45569, 45587, 45589, 45599, 45613, 45667, 45751, 45757, 45779, 45821, 45853, 45943, 45959, 45989, 46027, 46049, 46051, 46073, 46093, 46099, 46141, 46147, 46187, 46237, 46261, 46301, 46307, 46309, 46327, 46381, 46439, 46451, 46507, 46559, 46567, 46573, 46589, 46601, 46663, 46679, 46687, 46727, 46747, 46751, 46771, 46807, 46811, 46817, 46819, 46861, 46877, 46889, 46901, 47051, 47087, 47093, 47111, 47119, 47137, 47143, 47147, 47189, 47207, 47221, 47269, 47287, 47297, 47303, 47309, 47317, 47351, 47381, 47387, 47407, 47419, 47431, 47459, 47501, 47521, 47527, 47543, 47581, 47609, 47629, 47639, 47711, 47713, 47737, 47741, 47777, 47791, 47807, 47809, 47819, 47843, 47939, 47969, 48023, 48029, 48119, 48179, 48193, 48221, 48239, 48247, 48259, 48311, 48337, 48341, 48353, 48371, 48397, 48449, 48487, 48497, 48593, 48623, 48649, 48661, 48679, 48731, 48733, 48761, 48787, 48821, 48847, 48869, 48871, 48883, 48889, 48947, 48953, 48973, 49003, 49033, 49057, 49069, 49081, 49109, 49177, 49193, 49211, 49223, 49277, 49307, 49333, 49339, 49363, 49367, 49369, 49391, 49409, 49411, 49417, 49429, 49459, 49477, 49481, 49531, 49537, 49549, 49597, 49603, 49633, 49663, 49667, 49669, 49739, 49747, 49787, 49807, 49831, 49843, 49891, 49919, 49927, 49939, 50051, 50077, 50101, 50111, 50123, 50131, 50147, 50159, 50177, 50207, 50221, 50227, 50231, 50273, 50287, 50291, 50333, 50341, 50411, 50417, 50497, 50503, 50513, 50549, 50551, 50587, 50591, 50593, 50599, 50627, 50647, 50671, 50683, 50723, 50773, 50789, 50821, 50833, 50839, 50849, 50857, 50867, 50929, 50969, 50971, 51109, 51131, 51133, 51137, 51169, 51193, 51203, 51257, 51263, 51283, 51287, 51307, 51329, 51341, 51343, 51347, 51361, 51383, 51407, 51427, 51503, 51521, 51539, 51551, 51577, 51581, 51613, 51647, 51659, 51673, 51679, 51683, 51691, 51713, 51721, 51769, 51803, 51817, 51829, 51869, 51893, 51907, 51971, 51973, 51977, 52027, 52057, 52121, 52127, 52147, 52177, 52201, 52237, 52249, 52253, 52267, 52321, 52361, 52363, 52369, 52379, 52387, 52391, 52489, 52501, 52511, 52541, 52543, 52553, 52567, 52579, 52609, 52639, 52667, 52673, 52691, 52709, 52721, 52727, 52733, 52747, 52783, 52817, 52837, 52859, 52889, 52901, 52903, 52919, 52937, 52957, 52967, 52973, 52981, 53003, 53047, 53089, 53093, 53117, 53129, 53149, 53173, 53201, 53233, 53267, 53281, 53309, 53353, 53419, 53453, 53503, 53507, 53551, 53591, 53593, 53609, 53611, 53629, 53633, 53639, 53653, 53657, 53699, 53717, 53731, 53777, 53783, 53819, 53831, 53849, 53861, 53887, 53891, 53897, 53899, 53917, 53927, 53951, 53959, 53993, 54011, 54013, 54037, 54059, 54083, 54091, 54101, 54133, 54139, 54151, 54163, 54167, 54217, 54269, 54293, 54311, 54323, 54331, 54347, 54361, 54367, 54371, 54377, 54413, 54437, 54443, 54499, 54517, 54547, 54563, 54601, 54617, 54647, 54673, 54709, 54713, 54751, 54779, 54799, 54829, 54869, 54877, 54881, 54907, 54917, 54919, 54941, 54949, 54959, 54973, 54979, 54983, 55021, 55049, 55109, 55163, 55207, 55217, 55219, 55229, 55313, 55331, 55333, 55337, 55343, 55351, 55373, 55381, 55411, 55439, 55441, 55487, 55501, 55579, 55589, 55603, 55621, 55639, 55663, 55667, 55711, 55717, 55721, 55733, 55787, 55793, 55799, 55807, 55813, 55819, 55823, 55829, 55849, 55889, 55921, 55931, 55949, 56009, 56039, 56041, 56081, 56093, 56099, 56113, 56149, 56167, 56171, 56207, 56237, 56239, 56249, 56263, 56267, 56269, 56299, 56311, 56383, 56401, 56431, 56443, 56453, 56467, 56473, 56477, 56489, 56531, 56533, 56569, 56599, 56611, 56629, 56633, 56663, 56681, 56687, 56711, 56713, 56731, 56737, 56767, 56813, 56843, 56873, 56891, 56909, 56911, 56921, 56923, 56941, 56951, 56963, 56983, 56993, 56999, 57047, 57073, 57077, 57089, 57131, 57139, 57149, 57163, 57179, 57191, 57223, 57241, 57251, 57259, 57269, 57287, 57301, 57331, 57347, 57349, 57373, 57389, 57397, 57457, 57487, 57527, 57529, 57593, 57637, 57641, 57649, 57731, 57773, 57787, 57809, 57847, 57853, 57881, 57899, 57901, 57923, 57943, 57947, 57977, 58031, 58049, 58057, 58061, 58109, 58151, 58153, 58171, 58207, 58211, 58231, 58237, 58243, 58309, 58321, 58363, 58367, 58379, 58393, 58403, 58417, 58441, 58451, 58537, 58543, 58567, 58573, 58579, 58613, 58657, 58661, 58679, 58687, 58711, 58733, 58763, 58771, 58787, 58831, 58889, 58897, 58901, 58907, 58913, 58921, 58937, 58943, 58979, 59021, 59023, 59029, 59053, 59069, 59083, 59093, 59113, 59119, 59123, 59141, 59149, 59167, 59183, 59197, 59207, 59219, 59221, 59263, 59273, 59341, 59351, 59357, 59417, 59419, 59467, 59473, 59513, 59557, 59567, 59617, 59621, 59659, 59663, 59669, 59699, 59707, 59729, 59747, 59771, 59791, 59797, 59833, 59863, 59921, 59929, 59951, 59957, 59971, 59981, 60013, 60017, 60029, 60091, 60107, 60127, 60139, 60167, 60217, 60257, 60271, 60337, 60343, 60353, 60383, 60427, 60457, 60497, 60509, 60527, 60539, 60611, 60617, 60637, 60647, 60703, 60719, 60733, 60737, 60757, 60779, 60793, 60859, 60887, 60889, 60901, 60913, 60917, 60919, 60923, 60953, 61001, 61007, 61051, 61057, 61091, 61099, 61141, 61169, 61211, 61223, 61231, 61253, 61261, 61283, 61297, 61339, 61363, 61381, 61403, 61483, 61507, 61511, 61547, 61559, 61609, 61627, 61631, 61637, 61643, 61651, 61673, 61717, 61723, 61751, 61757, 61781, 61813, 61843, 61861, 61927, 61961, 61979, 61981, 61987, 61991, 62003, 62011, 62039, 62047, 62081, 62099, 62137, 62141, 62143, 62189, 62201, 62219, 62233, 62297, 62299, 62311, 62323, 62347, 62383, 62401, 62417, 62477, 62497, 62501, 62507, 62539, 62563, 62591, 62597, 62617, 62633, 62639, 62701, 62743, 62753, 62761, 62791, 62869, 62897, 62903, 62921, 62969, 62971, 62981, 62983, 63029, 63031, 63079, 63113, 63127, 63149, 63179, 63211, 63241 ] #I Prime powers to be sieved : 3157 #I Length of sieving interval : 524288 #I Small prime limit : 281 #I Large prime limit : 15903697 #I Number of used a - factors : 5 #I Size of a - factors pool : 68 #I a - factors pool : [ 498611, 498653, 498679, 498689, 498803, 498857, 498859, 498881, 498907, 498923, 498947, 498973, 498977, 498989, 499063, 499099, 499127, 499129, 499133, 499141, 499157, 499159, 499181, 499183, 499211, 499277, 499309, 499321, 499327, 499361, 499483, 499493, 499519, 499559, 499571, 499601, 499621, 499711, 499729, 499747, 499853, 499897, 499903, 499927, 499943, 499957, 499979, 500009, 500029, 500041, 500057, 500083, 500113, 500119, 500179, 500197, 500209, 500321, 500333, 500363, 500413, 500509, 500519, 500527, 500587, 500671, 500677, 500791 ] #I #I Sieving #I #I Collecting relations with a large factor #I Complete factorizations over the factor base : 100 #I Relations with a large prime factor : 16 #I Relations remaining to be found : 3116 #I Total factorizations with a large prime factor : 2086 #I Used Polynomials : 5322 #I Efficiency 1 : 7 % #I Efficiency 2 : 39 % #I Progress : 3 % #I #I #I Collecting relations with a large factor #I Complete factorizations over the factor base : 200 #I Relations with a large prime factor : 57 #I Relations remaining to be found : 2975 #I Total factorizations with a large prime factor : 4468 #I Used Polynomials : 11572 #I Efficiency 1 : 7 % #I Efficiency 2 : 38 % #I Progress : 7 % #I #I #I Collecting relations with a large factor #I Complete factorizations over the factor base : 300 #I Relations with a large prime factor : 146 #I Relations remaining to be found : 2786 #I Total factorizations with a large prime factor : 6729 #I Used Polynomials : 17576 #I Efficiency 1 : 7 % #I Efficiency 2 : 38 % #I Progress : 13 % #I #I #I Collecting relations with a large factor #I Complete factorizations over the factor base : 400 #I Relations with a large prime factor : 269 #I Relations remaining to be found : 2563 #I Total factorizations with a large prime factor : 9163 #I Used Polynomials : 23916 #I Efficiency 1 : 7 % #I Efficiency 2 : 38 % #I Progress : 20 % #I #I #I Collecting relations with a large factor #I Complete factorizations over the factor base : 500 #I Relations with a large prime factor : 391 #I Relations remaining to be found : 2341 #I Total factorizations with a large prime factor : 11215 #I Used Polynomials : 29391 #I Efficiency 1 : 7 % #I Efficiency 2 : 38 % #I Progress : 27 % #I #I #I Collecting relations with a large factor #I Complete factorizations over the factor base : 600 #I Relations with a large prime factor : 565 #I Relations remaining to be found : 2067 #I Total factorizations with a large prime factor : 13500 #I Used Polynomials : 35072 #I Efficiency 1 : 7 % #I Efficiency 2 : 38 % #I Progress : 36 % #I #I #I Collecting relations with a large factor #I Complete factorizations over the factor base : 700 #I Relations with a large prime factor : 736 #I Relations remaining to be found : 1796 #I Total factorizations with a large prime factor : 15530 #I Used Polynomials : 40518 #I Efficiency 1 : 7 % #I Efficiency 2 : 38 % #I Progress : 44 % #I #I #I Collecting relations with a large factor #I Complete factorizations over the factor base : 800 #I Relations with a large prime factor : 921 #I Relations remaining to be found : 1511 #I Total factorizations with a large prime factor : 17370 #I Used Polynomials : 45247 #I Efficiency 1 : 7 % #I Efficiency 2 : 38 % #I Progress : 53 % #I #I #I Collecting relations with a large factor #I Complete factorizations over the factor base : 900 #I Relations with a large prime factor : 1135 #I Relations remaining to be found : 1197 #I Total factorizations with a large prime factor : 19429 #I Used Polynomials : 50598 #I Efficiency 1 : 7 % #I Efficiency 2 : 38 % #I Progress : 62 % #I #I #I Collecting relations with a large factor #I Complete factorizations over the factor base : 1000 #I Relations with a large prime factor : 1385 #I Relations remaining to be found : 847 #I Total factorizations with a large prime factor : 21498 #I Used Polynomials : 56087 #I Efficiency 1 : 7 % #I Efficiency 2 : 38 % #I Progress : 73 % #I #I #I Collecting relations with a large factor #I Complete factorizations over the factor base : 1100 #I Relations with a large prime factor : 1700 #I Relations remaining to be found : 432 #I Total factorizations with a large prime factor : 23799 #I Used Polynomials : 61904 #I Efficiency 1 : 7 % #I Efficiency 2 : 38 % #I Progress : 86 % #I #I #I Collecting relations with a large factor #I Complete factorizations over the factor base : 1200 #I Relations with a large prime factor : 2013 #I Relations remaining to be found : 19 #I Total factorizations with a large prime factor : 26070 #I Used Polynomials : 68014 #I Efficiency 1 : 7 % #I Efficiency 2 : 38 % #I Progress : 99 % #I #I Creating the exponent matrix #I Doing Gaussian Elimination, #rows = 3232, #columns = 3212 #I Processing the zero rows #I Dependency no. 1 yielded factor 969330861796869994456492130438574359 #I The factors are [ 969330861796869994456492130438574359, 34316843565107624715057451342247 ] #I Intermediate result : [ [ 34316843565107624715057451342247, 969330861796869994456492130438574359 ], [ ] ] #I #I The result is [ [ 24325267, 34316843565107624715057451342247, 969330861796869994456492130438574359 ], [ ] ] gap>