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2020-07-10, 17:18   #879
sweety439

Nov 2016

44768 Posts

Quote:
 Originally Posted by sweety439 There are many Riesel case for k=64 (since 64 = 4^3 = 8^2, thus n == 0 mod 2 or n == 0 mod 3 have algebra factors: Bases 619, 1322, 2025, 2728, 3431, 4134, 4837, 5540, 6243, 6946, 7649, 8352, 9055, 9758, ...: n == 1 mod 3: factor of 19, n == 5 mod 6: factor of 37 Bases 429, 1816, 3203, 4590, 5977, 7364, 8751, ...: n == 1 mod 3: factor of 19, n == 2 mod 3: factor of 73 Bases 391, 2462, 4533, 6604, 8675, ...: n == 1 mod 3: factor of 19, n == 5 mod 6: factor of 109 Bases 159, 862, 1565, 2268, 2971, 3674, 4377, 5080, 5783, 6486, 7189, 7892, 8595, 9298, ...: n == 1 mod 6: factor of 37, n == 2 mod 3: factor of 19 Bases 1232, 3933, 6634, 9335, ...: n == 1 mod 6: factor of 37, n == 2 mod 3: factor of 73 Bases 936, 4969, 9002, ...: n == 1 mod 6: factor of 37, n == 5 mod 6: factor of 109 Bases 957, 2344, 3731, 5118, 6505, 7892, 9279, ...: n == 1 mod 3: factor of 73, n == 2 mod 3: factor of 19 Bases 1322, 4023, 6724, 9425, ...: n == 1 mod 3: factor of 73, n == 5 mod 6: factor of 37 Bases 4315, ...: n == 1 mod 3: factor of 73, n == 5 mod 6: factor of 109 Bases 482, 2553, 4624, 6695, 8766, ...: n == 1 mod 6: factor of 109, n == 2 mod 3: factor of 19 Bases 3098, 7131, ...: n == 1 mod 6: factor of 109, n == 5 mod 6: factor of 37 Bases 4079, ...: n == 1 mod 6: factor of 109, n == 2 mod 3: factor of 73
Also, for Sierpinski k=2500 (while n == 0 mod 4 have algebra factors)

These bases have (odd n has factor of 3 and n == 2 mod 4 has factor of 17):

38, 47, 89, 98, 140, 149, 191, 200, 242, 251, 293, 302, 344, 353, 395, 404, 446, 455, 497, 506, 548, 557, 599, 608, 650, 659, 701, 710, 752, 761, 803, 812, 854, 863, 905, 914, 956, 965, 1007, 1016, 1058, 1067, 1109, 1118, 1160, 1169, 1211, 1220, 1262, 1271, 1313, 1322, 1364, 1373, 1415, 1424, 1466, 1475, 1517, 1526, 1568, 1577, 1619, 1628, 1670, 1679, 1721, 1730, 1772, 1781, 1823, 1832, 1874, 1883, 1925, 1934, 1976, 1985, 2027, 2036, 2078, 2087, 2129, 2138, 2180, 2189, 2231, 2240, 2282, 2291, 2333, 2342, 2384, 2393, 2435, 2444, 2486, 2495, 2537, 2546, 2588, 2597, 2639, 2648, 2690, 2699, 2741, 2750, 2792, 2801, 2843, 2852, 2894, 2903, 2945, 2954, 2996, 3005, 3047, 3056, 3098, 3107, 3149, 3158, 3200, 3209, 3251, 3260, 3302, 3311, 3353, 3362, 3404, 3413, 3455, 3464, 3506, 3515, 3557, 3566, 3608, 3617, 3659, 3668, 3710, 3719, 3761, 3770, 3812, 3821, 3863, 3872, 3914, 3923, 3965, 3974, 4016, 4025, 4067, 4076, 4118, 4127, 4169, 4178, 4220, 4229, 4271, 4280, 4322, 4331, 4373, 4382, 4424, 4433, 4475, 4484, 4526, 4535, 4577, 4586, 4628, 4637, 4679, 4688, 4730, 4739, 4781, 4790, 4832, 4841, 4883, 4892, 4934, 4943, 4985, 4994, 5036, 5045, 5087, 5096, 5138, 5147, 5189, 5198, 5240, 5249, 5291, 5300, 5342, 5351, 5393, 5402, 5444, 5453, 5495, 5504, 5546, 5555, 5597, 5606, 5648, 5657, 5699, 5708, 5750, 5759, 5801, 5810, 5852, 5861, 5903, 5912, 5954, 5963, 6005, 6014, 6056, 6065, 6107, 6116, 6158, 6167, 6209, 6218, 6260, 6269, 6311, 6320, 6362, 6371, 6413, 6422, 6464, 6473, 6515, 6524, 6566, 6575, 6617, 6626, 6668, 6677, 6719, 6728, 6770, 6779, 6821, 6830, 6872, 6881, 6923, 6932, 6974, 6983, 7025, 7034, 7076, 7085, 7127, 7136, 7178, 7187, 7229, 7238, 7280, 7289, 7331, 7340, 7382, 7391, 7433, 7442, 7484, 7493, 7535, 7544, 7586, 7595, 7637, 7646, 7688, 7697, 7739, 7748, 7790, 7799, 7841, 7850, 7892, 7901, 7943, 7952, 7994, 8003, 8045, 8054, 8096, 8105, 8147, 8156, 8198, 8207, 8249, 8258, 8300, 8309, 8351, 8360, 8402, 8411, 8453, 8462, 8504, 8513, 8555, 8564, 8606, 8615, 8657, 8666, 8708, 8717, 8759, 8768, 8810, 8819, 8861, 8870, 8912, 8921, 8963, 8972, 9014, 9023, 9065, 9074, 9116, 9125, 9167, 9176, 9218, 9227, 9269, 9278, 9320, 9329, 9371, 9380, 9422, 9431, 9473, 9482, 9524, 9533, 9575, 9584, 9626, 9635, 9677, 9686, 9728, 9737, 9779, 9788, 9830, 9839, 9881, 9890, 9932, 9941, 9983, 9992, ...

These bases have (odd n has factor of 7 and n == 2 mod 4 has factor of 17):

13, 55, 132, 174, 251, 293, 370, 412, 489, 531, 608, 650, 727, 769, 846, 888, 965, 1007, 1084, 1126, 1203, 1245, 1322, 1364, 1441, 1483, 1560, 1602, 1679, 1721, 1798, 1840, 1917, 1959, 2036, 2078, 2155, 2197, 2274, 2316, 2393, 2435, 2512, 2554, 2631, 2673, 2750, 2792, 2869, 2911, 2988, 3030, 3107, 3149, 3226, 3268, 3345, 3387, 3464, 3506, 3583, 3625, 3702, 3744, 3821, 3863, 3940, 3982, 4059, 4101, 4178, 4220, 4297, 4339, 4416, 4458, 4535, 4577, 4654, 4696, 4773, 4815, 4892, 4934, 5011, 5053, 5130, 5172, 5249, 5291, 5368, 5410, 5487, 5529, 5606, 5648, 5725, 5767, 5844, 5886, 5963, 6005, 6082, 6124, 6201, 6243, 6320, 6362, 6439, 6481, 6558, 6600, 6677, 6719, 6796, 6838, 6915, 6957, 7034, 7076, 7153, 7195, 7272, 7314, 7391, 7433, 7510, 7552, 7629, 7671, 7748, 7790, 7867, 7909, 7986, 8028, 8105, 8147, 8224, 8266, 8343, 8385, 8462, 8504, 8581, 8623, 8700, 8742, 8819, 8861, 8938, 8980, 9057, 9099, 9176, 9218, 9295, 9337, 9414, 9456, 9533, 9575, 9652, 9694, 9771, 9813, 9890, 9932, ...