A Sierpinski/Riesel-like problem - Page 93

sweety439 · 2020-09-30, 16:15

Quote:

Originally Posted by sweety439

The CK for R420 is known to be 6548233
I have checked it.

Note: For the conjecture of R420, these k-values proven composite by partial algebra factors:

* k = m^2 with m = = 29 or 392 mod 421
* k = 105*m^2 with m = = 58 or 363 mod 421

Found two CK's:

R210 has CK = 50718493
R120 has CK = 166616308

The CK for S210 and S120 are still running ....

sweety439 · 2020-10-01, 10:27

Found two CK's:

S330 has CK = 11091478
R330 has CK = 11200379

sweety439 · 2020-10-01, 14:30

Quote:

Originally Posted by sweety439

Sierpinski k=1: {31, 38, 50, 55, 62, 63, 67, 68, 77, 83, 86, 89, 91, 92, 97, 98, 99, 104, 107, 109, 122, 123, 127, 135, 137, 143, 144, 147, 149, 151, 155, 161, 168, 179, 182, 183, 186, 189, 197, 200, 202, 207, 211, 212, 214, 215, 218, 223, 227, 233, 235, 241, 244, 246, 247, 249, 252, 255, 257, 258, 263, 265, 269, 281, 283, 285, 286, 287, 291, 293, 294, 298, 302, 303, 304, 307, 308, 311, 319, 322, 324, 327, 338, 344, 347, 351, 354, 355, 356, 359, 362, 367, 368, 369, 377, 380, 383, 387, 389, 390, 394, 398, 401, 402, 404, 407, 410, 411, 413, 416, 417, 422, 423, 424, 437, 439, 443, 446, 447, 450, 454, 458, 467, 468, 469, 473, 475, 480, 482, 483, 484, 489, 493, 495, 497, 500, 509, 511, 514, 515, 518, 524, 528, 530, 533, 534, 538, 547, 549, 552, 555, 558, 563, 564, 572, 574, 578, 580, 590, 591, 593, 597, 601, 602, 603, 604, 608, 611, 615, 619, 620, 622, 626, 627, 629, 632, 635, 637, 638, 645, 647, 648, 650, 651, 653, 655, 659, 662, 663, 666, 667, 668, 670, 671, 675, 678, 679, 683, 684, 687, 691, 692, 694, 698, 706, 707, 709, 712, 720, 722, 724, 731, 734, 735, 737, 741, 743, 744, 746, 749, 752, 753, 754, 755, 759, 762, 766, 767, 770, 771, 773, 775, 783, 785, 787, 792, 794, 797, 802, 806, 807, 809, 812, 813, 814, 818, 823, 825, 836, 840, 842, 844, 848, 849, 851, 853, 854, 867, 868, 870, 872, 873, 878, 887, 888, 889, 893, 896, 899, 902, 903, 904, 907, 908, 911, 915, 922, 923, 924, 926, 927, 932, 937, 938, 939, 941, 942, 943, 944, 945, 947, 948, 953, 954, 958, 961, 964, 967, 968, 974, 975, 977, 978, 980, 983, 987, 988, 993, 994, 998, 999, 1002, 1003, 1006, 1009, 1014, 1016} (totally 317 bases)

Sierpinski k=2: {365, 383, 461, 512, 542, 647, 773, 801, 829, 836, 859, 878, 908, 914, 917, 947, 1004, 1006} (totally 18 bases)

Sierpinski k=3: {83, 123, 191, 303, 323, 333, 363, 403, 453, 461, 483, 499, 511, 523, 683, 711, 718, 723, 743, 751, 779, 783, 807, 813, 823, 827, 847, 912, 979, 997, 1003, 1005, 1011, 1023} (totally 34 bases)

Sierpinski k=4: {32, 53, 155, 174, 204, 212, 230, 266, 281, 332, 334, 335, 356, 371, 386, 395, 467, 512, 593, 611, 661, 731, 767, 776, 803, 848, 851, 861, 875, 926, 941, 971, 981, 1024} (totally 34 bases)

Sierpinski k=5: {137, 183, 187, 193, 243, 305, 308, 415, 439, 512, 533, 545, 663, 667, 675, 761, 795, 809, 824, 835, 898, 941, 955, 997, 999, 1006} (totally 26 bases)

Sierpinski k=6: {212, 239, 509, 579, 625, 729, 774, 799, 894, 993, 999} (totally 11 bases)

Sierpinski k=7: {103, 255, 357, 387, 427, 477, 487, 573, 597, 687, 717, 735, 787, 807, 877, 895, 927, 939, 997, 1017} (totally 20 bases)

Sierpinski k=8: {86, 140, 163, 182, 235, 263, 328, 334, 349, 353, 368, 389, 391, 395, 422, 426, 428, 434, 443, 463, 488, 497, 558, 572, 575, 593, 606, 613, 658, 698, 710, 739, 746, 748, 758, 770, 773, 785, 790, 824, 828, 847, 866, 883, 908, 911, 930, 937, 953, 955, 957, 958, 983, 993, 1009, 1014} (totally 56 bases)

Sierpinski k=9: {167, 183, 187, 331, 383, 503, 555, 557, 576, 627, 643, 663, 683, 696, 724, 731, 751, 787, 829, 884, 903, 969, 1023} (totally 23 bases)

Sierpinski k=10: {185, 338, 417, 432, 614, 650, 668, 744, 773, 863, 914, 935, 977, 1000} (totally 14 bases)

Sierpinski k=11: {131, 243, 274, 355, 373, 560, 634, 682, 733, 743, 770, 813, 837, 877, 889, 895, 904, 933, 957, 958, 968, 997} (totally 22 bases)

Sierpinski k=12: {12, 163, 207, 354, 362, 368, 417, 480, 620, 692, 697, 736, 753, 792, 978, 998, 1019, 1022} (totally 18 bases)

sweety439 · 2020-10-01, 14:34

Links:

bases b<=128 and b = 256, 512, 1024; k < 1st CK

bases b<=64 (except 2, 3, 6, 15, 22, 24, 28, 30, 36, 40, 42, 46, 48, 52, 58, 60, 63 (which have larger CK)) and b = 100, 128, 256, 512, 1024; k < 4th CK

bases b<=32 and b = 64, 128, 256; k<=1024

bases b<=1024; k<=12

sweety439 · 2020-10-01, 14:36

First 4 Sierpinski conjectures:

Code:

b: first 4 CK
2: 78557, 157114, 271129, 271577,
3: 11047, 23789, 27221, 32549,
4: 419, 659, 794, 1466,
5: 7, 11, 31, 35,
6: 174308, 188299, 243417, 282001,
7: 209, 1463, 3305, 3533,
8: 47, 79, 83, 181,
9: 31, 39, 111, 119,
10: 989, 1121, 3653, 3662,
11: 5, 7, 17, 19,
12: 521, 597, 1143, 1509,
13: 15, 27, 47, 71,
14: 4, 11, 19, 26,
15: 673029, 2105431, 2692337, 4621459,
16: 38, 194, 524, 608,
17: 31, 47, 127, 143,
18: 398, 512, 571, 989,
19: 9, 11, 29, 31,
20: 8, 13, 29, 34,
21: 23, 43, 47, 111,
22: 2253, 4946, 6694, 8417,
23: 5, 7, 17, 19,
24: 30651, 66356, 77554, 84766,
25: 79, 103, 185, 287,
26: 221, 284, 1627, 1766,
27: 13, 15, 41, 43,
28: 4554, 8293, 13687, 18996,
29: 4, 7, 11, 19,
30: 867, 9859, 10386, 10570,
31: 239, 293, 521, 1025,
32: 10, 23, 43, 56,
33: 511, 543, 1599, 1631,
34: 6, 29, 41, 64,
35: 5, 7, 17, 19,
36: 1886, 11093, 67896, 123189,
37: 39, 75, 87, 191,
38: 14, 16, 25, 53,
39: 9, 11, 29, 31,
40: 47723, 67241, 68963, 133538,
41: 8, 13, 15, 23,
42: 13372, 30359, 47301, 60758,
43: 21, 23, 65, 67,
44: 4, 11, 19, 26,
45: 47, 91, 231, 275,
46: 881, 1592, 2519, 3104,
47: 5, 7, 8, 16,
48: 1219, 3403, 5531, 5613,
49: 31, 79, 179, 191,
50: 16, 35, 67, 86,
51: 25, 27, 77, 79,
52: 28674, 57398, 83262, 117396,
53: 7, 11, 31, 35,
54: 21, 34, 76, 89,
55: 13, 15, 41, 43,
56: 20, 37, 77, 94,
57: 47, 175, 231, 311,
58: 488, 1592, 7766, 8312,
59: 4, 5, 7, 9,
60: 16957, 84486, 138776, 199103,
61: 63, 123, 311, 371,
62: 8, 13, 29, 34,
63: 1589, 2381, 4827, 7083,
64: 14, 51, 79, 116,
65: 10, 23, 43, 56,
66:
67: 26, 33, 35, 101,
68: 22, 36, 47, 56,
69: 6, 15, 19, 27,
70: 11077, 20591, 22719, 25914,
71: 5, 7, 17, 19,
72: 731, 1313, 1461, 3724,
73: 47, 223, 255, 295,
74: 4, 11, 19, 26,
75: 37, 39, 113, 115,
76: 34, 43, 111, 120,
77: 7, 11, 14, 25,
78: 96144, 186123, 288507, 390656,
79: 9, 11, 29, 31,
80: 1039, 3181, 7438, 12211,
81: 575, 649, 655, 1167,
82: 19587, 29051, 37847, 46149,
83: 5, 7, 8, 13,
84: 16, 69, 101, 154,
85: 87, 171, 431, 515,
86: 28, 59, 115, 146,
87: 21, 23, 65, 67,
88: 26, 179, 311, 521,
89: 4, 11, 19, 23,
90: 27, 64, 118, 155,
91: 45, 47, 137, 139,
92: 32, 61, 125, 154,
93: 95, 187, 471, 563,
94: 39, 56, 134, 151,
95: 5, 7, 17, 19,
96: 68869, 353081, 426217, 427383,
97: 127, 223, 575, 671,
98: 10, 16, 23, 38,
99: 9, 11, 29, 31,
100: 62, 233, 332, 836,
101: 7, 11, 16, 31,
102: 293, 1342, 6060, 6240,
103: 25, 27, 77, 79,
104: 4, 6, 8, 11,
105: 319, 423, 1167, 1271,
106: 2387, 5480, 14819, 17207,
107: 5, 7, 17, 19,
108: 26270, 102677, 131564, 132872,
109: 19, 21, 23, 31,
110: 38, 73, 149, 184,
111: 13, 15, 41, 43,
112: 2261, 2939, 3502, 5988,
113: 20, 31, 37, 47,
114: 24, 91, 139, 206,
115: 57, 59, 173, 175,
116: 14, 25, 53, 64,
117: 119, 235, 327, 591,
118: 50, 69, 169, 188,
119: 4, 5, 7, 9,
120:
121: 27, 103, 110, 293,
122: 40, 47, 79, 83,
123: 55, 61, 63, 69,
124: 31001, 56531, 77381, 145994,
125: 7, 8, 11, 13,
126: 766700, 1835532, 2781934, 2986533,
127: 6343, 7909, 12923, 13701,
128: 44, 85, 98, 173,
129: 14, 51, 79, 116,
130: 1049, 2432, 7073, 9602,
131: 5, 7, 10, 17,
132: 13, 20, 113, 153,
133: 59, 135, 267, 671,
134: 4, 11, 19, 26,
135: 33, 35, 101, 103,
136: 29180, 90693, 151660, 243037,
137: 22, 23, 31, 47,
138: 2781, 3752, 4308, 7229,
139: 6, 9, 11, 13,
140: 46, 95, 187, 236,
141: 143, 283, 711, 851,
142: 12, 131, 155, 221,
143: 5, 7, 17, 19,
144: 59, 86, 204, 231,
145: 1023, 1167, 2159, 2367,
146: 8, 13, 29, 34,
147: 73, 75, 221, 223,
148: 3128, 4022, 4471, 7749,
149: 4, 7, 11, 19,
150: 49074, 95733, 539673, 611098,
151: 37, 39, 113, 115,
152: 16, 35, 67, 86,
153: 15, 34, 43, 55,
154: 61, 94, 216, 249,
155: 5, 7, 14, 17,
156:
157: 47, 59, 159, 191,
158: 52, 107, 122, 211,
159: 9, 11, 29, 31,
160: 22, 139, 183, 300,
161: 95, 127, 287, 319,
162: 6193, 6682, 7336, 14343,
163: 81, 83, 245, 247,
164: 4, 10, 11, 19,
165: 167, 331, 831, 995,
166: 335, 5510, 7349, 9854,
167: 5, 7, 8, 13,
168: 9244, 9658, 15638, 20357,
169: 16, 31, 39, 69,
170: 20, 37, 77, 94,
171: 85, 87, 257, 259,
172: 62, 108, 836, 1070,
173: 7, 11, 28, 31,
174: 6, 29, 41, 64,
175: 21, 23, 65, 67,
176: 58, 119, 235, 296,
177: 79, 447, 1247, 1423,
178: 569, 797, 953, 1031,
179: 4, 5, 7, 9,
180: 1679679,
181: 15, 27, 51, 64,
182: 23, 62, 121, 211,
183: 45, 47, 69, 101,
184: 36, 149, 221, 269,
185: 23, 31, 32, 61,
186: 67, 120, 254, 307,
187: 47, 83, 93, 95,
188: 8, 13, 29, 34,
189: 19, 31, 39, 56,
190: 2157728, 3146151, 3713039, 4352889,
191: 5, 7, 17, 19,
192: 7879, 8686, 17371, 19494,
193: 2687, 6015, 6207, 9343,
194: 4, 11, 14, 19,
195: 13, 15, 41, 43,
196: 16457, 78689, 86285, 95147,
197: 7, 10, 11, 23,
198: 4105, 19484, 21649, 23581,
199: 9, 11, 29, 31,
200: 47, 68, 103, 118,
201: 607, 807, 2223, 2423,
202: 57, 146, 260, 349,
203: 5, 7, 16, 17,
204: 81, 124, 286, 329,
205: 207, 411, 1031, 1235,
206: 22, 47, 91, 116,
207: 25, 27, 77, 79,
208: 56, 98, 153, 265,
209: 4, 6, 8, 11,
210:
211: 105, 107, 317, 319,
212: 70, 143, 283, 285,
213: 51, 215, 339, 427,
214: 44, 171, 236, 259,
215: 5, 7, 17, 19,
216: 92, 125, 309, 342,
217: 655, 863, 871, 919,
218: 74, 145, 293, 364,
219: 9, 11, 21, 23,
220: 50, 103, 118, 324,
221: 7, 11, 31, 35,
222: 333163, 352341, 389359, 410098,
223: 13, 15, 41, 43,
224: 4, 11, 19, 26,
225: 3391, 3615, 10623, 10847,
226: 2915, 11744, 12563, 15704,
227: 5, 7, 17, 19,
228: 1146, 7098, 8474, 25647,
229: 19, 24, 31, 47,
230: 8, 10, 13, 23,
231: 57, 59, 173, 175,
232: 2564, 18992, 27527, 46520,
233: 14, 23, 25, 31,
234: 46, 189, 281, 424,
235: 107, 117, 119, 255,
236: 80, 157, 317, 394,
237: 15, 27, 50, 67,
238: 34571, 36746, 42449, 48038,
239: 4, 5, 7, 9,
240: 1722187, 1933783, 2799214,
241: 175, 287, 527, 639,
242: 8, 16, 38, 47,
243: 121, 123, 285, 365,
244: 6, 29, 41, 64,
245: 7, 11, 31, 35,
246: 77, 170, 324, 417,
247: 61, 63, 185, 187,
248: 82, 167, 331, 416,
249: 31, 39, 111, 119,
250: 9788, 23885, 33539, 50450,
251: 5, 7, 8, 13,
252: 45, 116, 144, 208,
253: 255, 327, 507, 691,
254: 4, 11, 16, 19,
255: 245, 365, 493, 499,
256: 38, 194, 467, 524,
512: 18, 20, 37, 47,
1024: 81, 124, 286, 329,
2048: 334, 682, 857, 1367,
4096: 656, 1206, 2330, 2564,
8192: 83, 182, 211, 319,
16384: 59, 86, 114, 204,
32768: 10, 23, 40, 43,
65536: 38, 62, 194, 230,

First 4 Riesel conjectures:

Code:

b: first 4 CK
2: 509203, 762701, 777149, 784109,
3: 12119, 20731, 21997, 28297,
4: 361, 919, 1114, 1444,
5: 13, 17, 37, 41,
6: 84687, 133946, 176602, 213410,
7: 457, 1291, 3199, 3313,
8: 14, 112, 116, 148,
9: 41, 49, 74, 121,
10: 334, 1585, 1882, 3340,
11: 5, 7, 17, 19,
12: 376, 742, 1288, 1364,
13: 29, 41, 69, 85,
14: 4, 11, 19, 26,
15: 622403, 1346041, 2742963,
16: 100, 172, 211, 295,
17: 49, 59, 65, 86,
18: 246, 664, 723, 837,
19: 9, 11, 29, 31,
20: 8, 13, 29, 34,
21: 45, 65, 133, 153,
22: 2738, 4461, 6209, 8902,
23: 5, 7, 17, 19,
24: 32336, 69691, 109054, 124031,
25: 105, 129, 211, 313,
26: 149, 334, 1892, 1987,
27: 13, 15, 41, 43,
28: 3769, 9078, 14472, 18211,
29: 4, 9, 11, 13,
30: 4928, 5331, 7968, 8958,
31: 145, 265, 443, 493,
32: 10, 23, 43, 56,
33: 545, 577, 764, 1633,
34: 6, 29, 41, 64,
35: 5, 7, 17, 19,
36: 33791, 79551, 89398, 116364,
37: 29, 77, 113, 163,
38: 13, 14, 25, 53,
39: 9, 11, 29, 31,
40: 25462, 29437, 38539, 52891,
41: 8, 13, 17, 25,
42: 15137, 28594, 45536, 62523,
43: 21, 23, 65, 67,
44: 4, 11, 19, 26,
45: 93, 137, 277, 321,
46: 928, 3754, 4078, 4636,
47: 5, 7, 13, 14,
48: 3226, 4208, 7029, 7965,
49: 81, 129, 229, 241,
50: 16, 35, 67, 86,
51: 25, 27, 77, 79,
52: 25015, 25969, 35299, 60103,
53: 13, 17, 37, 41,
54: 21, 34, 76, 89,
55: 13, 15, 41, 43,
56: 20, 37, 77, 94,
57: 144, 177, 233, 289,
58: 547, 919, 1408, 1957,
59: 4, 5, 7, 9,
60: 20558, 80885, 135175, 202704,
61: 125, 185, 373, 433,
62: 8, 13, 29, 34,
63: 857, 3113, 5559, 6351,
64: 14, 51, 79, 116,
65: 10, 23, 43, 56,
66:
67: 33, 35, 37, 101,
68: 22, 43, 47, 61,
69: 6, 9, 21, 29,
70: 853, 4048, 6176, 15690,
71: 5, 7, 17, 19,
72: 293, 2481, 3722, 4744,
73: 112, 177, 297, 329,
74: 4, 11, 19, 26,
75: 37, 39, 113, 115,
76: 34, 43, 111, 120,
77: 13, 14, 17, 25,
78: 90059, 192208, 294592, 384571,
79: 9, 11, 29, 31,
80: 253, 1037, 6148, 11765,
81: 74, 575, 657, 737,
82: 22326, 36438, 44572, 64905,
83: 5, 7, 8, 13,
84: 16, 69, 101, 154,
85: 173, 257, 517, 601,
86: 28, 59, 115, 146,
87: 21, 23, 65, 67,
88: 571, 862, 898, 961,
89: 4, 11, 17, 19,
90: 27, 64, 118, 155,
91: 45, 47, 137, 139,
92: 32, 61, 125, 154,
93: 189, 281, 565, 612,
94: 39, 56, 134, 151,
95: 5, 7, 17, 19,
96: 38995, 78086, 343864, 540968,
97: 43, 225, 321, 673,
98: 10, 23, 43, 56,
99: 9, 11, 29, 31,
100: 211, 235, 334, 750,
101: 13, 16, 17, 33,
102: 1635, 1793, 4267, 4447,
103: 25, 27, 77, 79,
104: 4, 6, 8, 11,
105: 297, 425, 529, 1273,
106: 13624, 14926, 16822, 19210,
107: 5, 7, 17, 19,
108: 13406, 26270, 43601, 103835,
109: 9, 21, 34, 45,
110: 38, 73, 149, 184,
111: 13, 15, 41, 43,
112: 1357, 3843, 4406, 5084,
113: 20, 37, 49, 65,
114: 24, 91, 139, 206,
115: 57, 59, 173, 175,
116: 14, 25, 53, 64,
117: 149, 221, 237, 353,
118: 50, 69, 169, 188,
119: 4, 5, 7, 9,
120:
121: 100, 163, 211, 232,
122: 14, 40, 83, 112,
123: 13, 61, 63, 154,
124: 92881, 104716, 124009, 170386,
125: 8, 13, 17, 29,
126: 480821, 2767077, 3925190,
127: 2593, 3251, 3353, 6451,
128: 44, 59, 85, 86,
129: 14, 51, 79, 116,
130: 2563, 5896, 11134, 26632,
131: 5, 7, 10, 17,
132: 20, 69, 113, 153,
133: 17, 233, 269, 273,
134: 4, 11, 19, 26,
135: 33, 35, 101, 103,
136: 22195, 47677, 90693, 151660,
137: 17, 22, 25, 47,
138: 1806, 4727, 5283, 6254,
139: 6, 9, 11, 13,
140: 46, 95, 187, 236,
141: 285, 425, 853, 993,
142: 12, 131, 155, 219,
143: 5, 7, 17, 19,
144: 59, 86, 204, 231,
145: 1169, 1313, 3505, 3649,
146: 8, 13, 29, 34,
147: 73, 75, 221, 223,
148: 1936, 5214, 5663, 6557,
149: 4, 9, 11, 13,
150: 49074, 95733, 228764, 539673,
151: 37, 39, 113, 115,
152: 16, 35, 67, 86,
153: 34, 43, 57, 65,
154: 61, 94, 216, 249,
155: 5, 7, 14, 17,
156:
157: 17, 69, 101, 217,
158: 52, 107, 211, 266,
159: 9, 11, 29, 31,
160: 22, 139, 183, 253,
161: 65, 97, 257, 289,
162: 3259, 4726, 9292, 16299,
163: 81, 83, 245, 247,
164: 4, 10, 11, 19,
165: 79, 333, 497, 646,
166: 4174, 9019, 11023, 15532,
167: 5, 7, 8, 13,
168: 4744, 14676, 15393, 20827,
169: 16, 33, 41, 49,
170: 20, 37, 77, 94,
171: 85, 87, 257, 259,
172: 235, 982, 1108, 1171,
173: 13, 17, 28, 37,
174: 6, 21, 29, 41,
175: 21, 23, 65, 67,
176: 58, 119, 235, 296,
177: 209, 268, 577, 1156,
178: 22, 79, 87, 334,
179: 4, 5, 7, 9,
180:
181: 25, 27, 29, 41,
182: 62, 121, 245, 304,
183: 45, 47, 137, 139,
184: 36, 149, 221, 334,
185: 17, 25, 32, 61,
186: 67, 120, 254, 307,
187: 51, 79, 93, 95,
188: 8, 13, 29, 34,
189: 9, 21, 39, 49,
190: 626861, 2121627, 3182252, 3749140,
191: 5, 7, 17, 19,
192: 13897, 19492, 20459, 22968,
193: 484, 5350, 6209, 6401,
194: 4, 11, 14, 19,
195: 13, 15, 41, 43,
196: 1267, 16654, 17920, 20692,
197: 10, 13, 17, 23,
198: 3662, 8425, 10546, 13224,
199: 9, 11, 29, 31,
200: 68, 133, 268, 269,
201: 809, 1009, 2425, 2625,
202: 57, 146, 260, 349,
203: 5, 7, 14, 16,
204: 81, 124, 286, 329,
205: 25, 361, 413, 617,
206: 22, 47, 91, 116,
207: 25, 27, 77, 79,
208: 56, 153, 186, 265,
209: 4, 6, 8, 11,
210:
211: 100, 105, 107, 317,
212: 70, 143, 149, 179,
213: 57, 73, 181, 429,
214: 44, 171, 259, 386,
215: 5, 7, 17, 19,
216: 92, 125, 309, 342,
217: 337, 353, 409, 441,
218: 74, 145, 293, 364,
219: 9, 11, 21, 23,
220: 103, 118, 324, 339,
221: 13, 17, 37, 38,
222: 88530, 90091, 282094, 514016,
223: 13, 15, 41, 43,
224: 4, 11, 19, 26,
225: 3617, 3841, 10849, 11073,
226: 820, 12790, 50257, 53398,
227: 5, 7, 17, 19,
228: 16718, 33891, 35267, 41219,
229: 9, 21, 24, 49,
230: 8, 10, 13, 23,
231: 57, 59, 173, 175,
232: 27760, 72817, 98791, 100576,
233: 14, 17, 25, 53,
234: 46, 189, 281, 424,
235: 64, 117, 119, 172,
236: 80, 157, 317, 394,
237: 29, 33, 41, 50,
238: 17926, 34810, 93628, 99094,
239: 4, 5, 7, 9,
240: 2952972, 2985025, 3695736, 4812046,
241: 65, 177, 417, 529,
242: 14, 73, 101, 116,
243: 121, 123, 365, 367,
244: 6, 29, 41, 64,
245: 13, 17, 37, 40,
246: 77, 170, 324, 417,
247: 61, 63, 185, 187,
248: 82, 167, 331, 416,
249: 41, 49, 121, 129,
250: 9655, 10039, 19828, 23344,
251: 5, 7, 8, 13,
252: 45, 47, 177, 208,
253: 149, 221, 509, 697,
254: 4, 11, 16, 19,
255: 73, 993, 1559, 1639,
256: 100, 172, 211, 295,
512: 14, 20, 37, 38,
1024: 81, 121, 124, 169,
2048: 29, 682, 1367, 1528,
4096: 172, 334, 343, 676,
8192: 28, 158, 476, 584,
16384: 59, 86, 114, 204,
32768: 10, 14, 23, 43,
65536: 100, 172, 211, 295,

sweety439 · 2020-10-01, 14:40

Quote:

Originally Posted by sweety439

Found two CK's:

S330 has CK = 11091478
R330 has CK = 11200379

Found two CK's:

S358 has CK = 9330411
R358 has CK = 9202246

sweety439 · 2020-10-02, 04:40

Found two CK's:

S210 has CK = 147840103
R570 has CK = 12511182

S120 and R946 are still running ....

sweety439 · 2020-10-02, 05:07

Reserving SR456

R946 has larger CK, compare with S946, which has CK = 3963194 and covering set {3, 13, 73, 373, 947}, period = 12

Bases with CK > 5M are:

66 (both sides, Sierpinski CK is known to be 21314443 and Riesel CK is known to be 63717671)

120 (both sides, Sierpinski CK is unknown and Riesel CK is known to be 166616308)

156 (both sides, CK for both sides are both unknown)

180 (Riesel side, CK = 7674582, the CK for Sierpinski side is only 1679679)

210 (both sides, Sierpinski CK is known to be 147840103 and Riesel CK is known to be 50718493)

280 (both sides, CK for both sides are both unknown)

330 (both sides, Sierpinski CK is known to be 11091478 and Riesel CK is known to be 11200379)

358 (both sides, Sierpinski CK is known to be 9330411 and Riesel CK is known to be 9202246)

420 (Riesel side, CK = 6548233, the CK for Sierpinski side is only 2288555)

456 (both sides, CK for both sides are now reserving ....)

462 (Sierpinski side, CK = 6880642, the CK for Riesel side is only 2924772)

546 (reserved)

570 (Riesel side, CK = 12511182, the CK for Sierpinski side is only 2972056)

630 (reserved)

690 (reserved)

726 (reserved)

728 (the original CK for both sides are both wrong, since the covering sets for the true CK for both sides have a large prime (105997), thus I didn't find them, the CK for the Sierpinski side is 953974 and the CK for the Riesel side is 212722)

756 (reserved)

876 (reserved)

910 (both sides, CK for both sides are both unknown)

946 (Riesel side, CK is now reserving, the CK for Sierpinski side is only 3963194)

960 (both sides, CK for both sides are both unknown)

966 (reserved)

1008 (Sierpinski side, CK is now reserving, the CK for Riesel side is only 623563)

1020 (reserved)

* Note: I will not reserve bases 156, 280, 910, and 960, since the upper bound of the CK for these bases (for both sides) are too large.

sweety439 · 2020-10-02, 05:22

For integer triple (k,b,c) such that k>=1, b>=2, c != 0, gcd(k,c) = 1, gcd(b,c) = 1, if there exist (positive or negative or 0) integer n such that

* either numerator((k*b^n+c)/gcd(k+c,b-1)) = +-1, or all prime factors of numerator((k*b^n+c)/gcd(k+c,b-1)) are factors of b

* for all integer r>1, k*b^n and -c are not both r-th powers of rational numbers

* k*b^n*c is not of the form 4*m^4 with rational number m

then there are (conjectured) infinitely many primes of the form (k*b^n+c)/gcd(k+c,b-1) with n>=1, since the sequence of the smallest prime factor of (k*b^n+c)/gcd(k+c,b-1) when n runs the integers such that (k*b^n+c)/gcd(k+c,b-1) has no algebra factors, is unbounded above (note that this does not include the case such that (k*b^n+c)/gcd(k+c,b-1) has algebra factors for all n, e.g. 4*9^n-1 and 9*4^n-1, since the upper bound of the empty set is -infinity, but a set is unbounded above if and only if the upper bound of this set is +infinitely, and -infinity != +infinity)

sweety439 · 2020-10-02, 12:28

Quote:

Originally Posted by sweety439

Found two CK's:

S210 has CK = 147840103
R570 has CK = 12511182

S120 and R946 are still running ....

Found two CK's:

S456 has CK = 14836963
R456 has CK = 14629026

sweety439 · 2020-10-03, 05:29

Found two CK's:

S546 has CK = 45119296
R546 has CK = 11732602

2020-10-02, 05:22	#1021
sweety439 "99(4^34019)99 palind" Nov 2016 (P^81993)SZ base 36 2·13·113 Posts	For integer triple (k,b,c) such that k>=1, b>=2, c != 0, gcd(k,c) = 1, gcd(b,c) = 1, if there exist (positive or negative or 0) integer n such that * either numerator((kb^n+c)/gcd(k+c,b-1)) = +-1, or all prime factors of numerator((kb^n+c)/gcd(k+c,b-1)) are factors of b * for all integer r>1, kb^n and -c are not both r-th powers of rational numbers kb^nc is not of the form 4m^4 with rational number m then there are (conjectured) infinitely many primes of the form (kb^n+c)/gcd(k+c,b-1) with n>=1, since the sequence of the smallest prime factor of (kb^n+c)/gcd(k+c,b-1) when n runs the integers such that (kb^n+c)/gcd(k+c,b-1) has no algebra factors, is unbounded above (note that this does not include the case such that (kb^n+c)/gcd(k+c,b-1) has algebra factors for all n, e.g. 49^n-1 and 94^n-1, since the upper bound of the empty set is -infinity, but a set is unbounded above if and only if the upper bound of this set is +infinitely, and -infinity != +infinity) Last fiddled with by sweety439 on 2020-10-02 at 05:38*

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2020-10-01, 10:27	#1014
sweety439 "99(4^34019)99 palind" Nov 2016 (P^81993)SZ base 36 2938₁₀ Posts	Found two CK's: S330 has CK = 11091478 R330 has CK = 11200379

2020-10-01, 14:34	#1016
sweety439 "99(4^34019)99 palind" Nov 2016 (P^81993)SZ base 36 2×13×113 Posts	Links: bases b<=128 and b = 256, 512, 1024; k < 1st CK bases b<=64 (except 2, 3, 6, 15, 22, 24, 28, 30, 36, 40, 42, 46, 48, 52, 58, 60, 63 (which have larger CK)) and b = 100, 128, 256, 512, 1024; k < 4th CK bases b<=32 and b = 64, 128, 256; k<=1024 bases b<=1024; k<=12

2020-10-02, 04:40	#1019
sweety439 "99(4^34019)99 palind" Nov 2016 (P^81993)SZ base 36 5572₈ Posts	Found two CK's: S210 has CK = 147840103 R570 has CK = 12511182 S120 and R946 are still running ....

2020-10-02, 05:07	#1020
sweety439 "99(4^34019)99 palind" Nov 2016 (P^81993)SZ base 36 2938₁₀ Posts	Reserving SR456 R946 has larger CK, compare with S946, which has CK = 3963194 and covering set {3, 13, 73, 373, 947}, period = 12 Bases with CK > 5M are: 66 (both sides, Sierpinski CK is known to be 21314443 and Riesel CK is known to be 63717671) 120 (both sides, Sierpinski CK is unknown and Riesel CK is known to be 166616308) 156 (both sides, CK for both sides are both unknown) 180 (Riesel side, CK = 7674582, the CK for Sierpinski side is only 1679679) 210 (both sides, Sierpinski CK is known to be 147840103 and Riesel CK is known to be 50718493) 280 (both sides, CK for both sides are both unknown) 330 (both sides, Sierpinski CK is known to be 11091478 and Riesel CK is known to be 11200379) 358 (both sides, Sierpinski CK is known to be 9330411 and Riesel CK is known to be 9202246) 420 (Riesel side, CK = 6548233, the CK for Sierpinski side is only 2288555) 456 (both sides, CK for both sides are now reserving ....) 462 (Sierpinski side, CK = 6880642, the CK for Riesel side is only 2924772) 546 (reserved) 570 (Riesel side, CK = 12511182, the CK for Sierpinski side is only 2972056) 630 (reserved) 690 (reserved) 726 (reserved) 728 (the original CK for both sides are both wrong, since the covering sets for the true CK for both sides have a large prime (105997), thus I didn't find them, the CK for the Sierpinski side is 953974 and the CK for the Riesel side is 212722) 756 (reserved) 876 (reserved) 910 (both sides, CK for both sides are both unknown) 946 (Riesel side, CK is now reserving, the CK for Sierpinski side is only 3963194) 960 (both sides, CK for both sides are both unknown) 966 (reserved) 1008 (Sierpinski side, CK is now reserving, the CK for Riesel side is only 623563) 1020 (reserved) * Note: I will not reserve bases 156, 280, 910, and 960, since the upper bound of the CK for these bases (for both sides) are too large.

2020-10-03, 05:29	#1023
sweety439 "99(4^34019)99 palind" Nov 2016 (P^81993)SZ base 36 2·13·113 Posts	Found two CK's: S546 has CK = 45119296 R546 has CK = 11732602