mersenneforum.org - A Sierpinski/Riesel-like problem

mersenneforum.org (https://www.mersenneforum.org/index.php)

- sweety439 (https://www.mersenneforum.org/forumdisplay.php?f=137)

- - A Sierpinski/Riesel-like problem (https://www.mersenneforum.org/showthread.php?t=21839)

For such (k,b) pair, k is Sierpinski number base b:

[CODE]
k b covering set
= 5, 7 mod 12 = 11 mod 12 {2, 3}
= 4, 11 mod 15 = 14 mod 15 {3, 5}
= 9, 11 mod 20 = 19 mod 20 {2, 5}
= 8, 13 mod 21 = 20 mod 21 {3, 7}
= 7, 11 mod 24 = 5 mod 24 {2, 3}
= 13, 15 mod 28 = 27 mod 28 {2, 7}
= 10, 23 mod 33 = 32 mod 33 {3, 11}
= 6, 29 mod 35 = 34 mod 35 {5, 7}
= 14, 25 mod 39 = 38 mod 39 {3, 13}
= 19, 31 mod 40 = 29 mod 40 {2, 5}
= 15, 27 mod 56 = 13 mod 56 {2, 7}
= 31, 39 mod 80 = 9 mod 80 {2, 5}
= 23, 43 mod 88 = 21 mod 88 {2, 11}
= 31, 47 mod 96 = 17 mod 96 {2, 3}
= 12, 131 mod 143 = 142 mod 143 {11, 13}
= 39, 75 mod 152 = 37 mod 152 {2, 19}
= 47, 79, 83, 181 mod 195 = 8, 122 mod 195 {3, 5, 13}
= 79, 103 mod 208 = 25 mod 208 {2, 13}
[/CODE]

[URL="https://github.com/xayahrainie4793/first-4-Sierpinski-Riesel-conjectures"]https://github.com/xayahrainie4793/first-4-Sierpinski-Riesel-conjectures[/URL]

For such (k,b) pair, k is Riesel number base b:

[CODE]
k b covering set
= 5, 7 mod 12 = 11 mod 12 {2, 3}
= 4, 11 mod 15 = 14 mod 15 {3, 5}
= 9, 11 mod 20 = 19 mod 20 {2, 5}
= 8, 13 mod 21 = 20 mod 21 {3, 7}
= 13, 17 mod 24 = 5 mod 24 {2, 3}
= 13, 15 mod 28 = 27 mod 28 {2, 7}
= 10, 23 mod 33 = 32 mod 33 {3, 11}
= 6, 29 mod 35 = 34 mod 35 {5, 7}
= 14, 25 mod 39 = 38 mod 39 {3, 13}
= 9, 21 mod 40 = 29 mod 40 {2, 5}
= 29, 41 mod 56 = 13 mod 56 {2, 7}
= 41, 49 mod 80 = 9 mod 80 {2, 5}
= 45, 65 mod 88 = 21 mod 88 {2, 11}
= 49, 65 mod 96 = 17 mod 96 {2, 3}
= 12, 131 mod 143 = 142 mod 143 {11, 13}
= 77, 113 mod 152 = 37 mod 152 {2, 19}
= 14, 112, 116, 148 mod 195 = 8, 122 mod 195 {3, 5, 13}
= 105, 129 mod 208 = 25 mod 208 {2, 13}
[/CODE]

Multiples of the base (MOB) are NOT excluded from the conjectures. They are excluded from the TESTING of the conjectures if and only if (k+-1)/gcd(k+-1,b-1) (+ for Sierpinski, - for Riesel) is not prime. Previously they were shown as being excluded from the conjectures.

That is, if k=4*b is eliminated because it is a MOB and k=4 has algebraic factors to make a full covering set, which of the two takes priority for k=4*b since it would also have algebraic factors to make a full covering set? The answer is algebraic factors take priority because k=4 cannot ever have a prime and so k=4*b must still be accounted for. SO: k=4*b has to be shown with algebraic factors because it too cannot ever have a prime.

This is certainly mathematical pickiness but to account for all k's, you can't just say a k is eliminated from the conjecture because it is a MOB and (k+-1)/gcd(k+-1,b-1) (+ for Sierpinski, - for Riesel) is not prime. The k still remains; it's just not shown as remaining or tested because k/b should eventually (or already has) yield the same prime. But if k/b can never have a prime than you must account for k.

Update the file of the first 3 conjectures to include these (probable) primes:

1037*12^6281-1 (see post [URL="https://mersenneforum.org/showpost.php?p=468841&postcount=466"]#466[/URL])

563*12^4020+1 (see post [URL="https://mersenneforum.org/showpost.php?p=468771&postcount=462"]#462[/URL])

(3356*10^4584+1)/9 (see post [URL="https://mersenneforum.org/showpost.php?p=469198&postcount=471"]#471[/URL])

(846*12^1384+1)/11 (see post [URL="https://mersenneforum.org/showpost.php?p=490257&postcount=655"]#655[/URL])

1057*12^690+1 and 1052*12^5715+1 (see post [URL="https://mersenneforum.org/showpost.php?p=490354&postcount=665"]#665[/URL])

Also the test limit:

R12 k=1132: n=21760 (see [URL="https://mersenneforum.org/showpost.php?p=490302&postcount=664"]https://mersenneforum.org/showpost.php?p=490302&postcount=664[/URL])

S10 k=1343 and 2573: n=15000 (see [URL="https://mersenneforum.org/showpost.php?p=469566&postcount=473"]https://mersenneforum.org/showpost.php?p=469566&postcount=473[/URL])

S12 k = 885, 911, 976, 1041: n=25000 (see [URL="https://mersenneforum.org/showpost.php?p=490354&postcount=665"]https://mersenneforum.org/showpost.php?p=490354&postcount=665[/URL])

Upload the zip file of the first 4 Sierpinski/Riesel conjectures, see [URL="https://github.com/xayahrainie4793/first-4-Sierpinski-Riesel-conjectures"]https://github.com/xayahrainie4793/first-4-Sierpinski-Riesel-conjectures[/URL]

(9216*96^3341-1)/gcd(9216-1,96-1) = (96^3343-1)/95 is (probable) prime

k=9216 eliminated from R96

[URL="https://docs.google.com/document/d/e/2PACX-1vTapltXh2uleqU5-JEGdQmRhGno_omtL23dlo3KZlolpjXieGCe8BV9SzYSXUMQWpeUFOz8vn2qiUhR/pub"]Newest status of Riesel problems[/URL]

See [URL="https://github.com/xayahrainie4793/first-4-Sierpinski-Riesel-conjectures"]https://github.com/xayahrainie4793/first-4-Sierpinski-Riesel-conjectures[/URL] for the status of the 1st, 2nd, 3rd, and 4th Sierpinski/Riesel problems.

[CODE]
base: conjectured first 16 Sierpinski k
2: 78557, 157114, 271129, 271577, 314228, 322523, 327739, 482719, 542258, 543154, 575041, 603713, 628456, 645046, 655478, 903983,
3: 11047, 23789, 27221, 32549, 33141, 40247, 47969, 66869, 67747, 70381, 70667, 71367, 78283, 79141, 81241, 81663,
4: 419, 659, 794, 1466, 1676, 1769, 2246, 2414, 2609, 2636, 2651, 2981, 3176, 3734, 4514, 4889,
5: 7, 11, 31, 35, 55, 59, 79, 83, 103, 107, 127, 131, 151, 155, 175, 179,
6: 174308, 188299, 243417, 282001, 464437, 702703, 715175, 1045848, 1100966, 1128499, 1129794, 1161910, 1293662, 1434861, 1446213, 1460502,
7: 209, 1463, 3305, 3533, 3827, 5927, 7703, 9461, 9683, 10241, 10658, 10781, 12077, 12463, 12643, 14243,
8: 47, 79, 83, 181, 242, 274, 278, 376, 437, 469, 473, 571, 632, 664, 668, 766,
9: 31, 39, 111, 119, 191, 199, 271, 279, 351, 359, 431, 439, 511, 519, 591, 599,
10: 989, 1121, 3653, 3662, 8207, 9175, 9351, 9593, 9890, 10313, 11177, 11210, 12221, 13355, 14849, 16028,
11: 5, 7, 17, 19, 29, 31, 41, 43, 53, 55, 65, 67, 77, 79, 89, 91,
12: 521, 597, 1143, 1509, 2406, 2482, 3028, 3394, 4291, 4367, 4913, 5279, 6176, 6252, 6798, 7164,
13: 15, 27, 47, 71, 83, 127, 132, 139, 183, 195, 239, 251, 293, 295, 307, 351,
14: 4, 11, 19, 26, 34, 41, 49, 56, 64, 71, 79, 86, 94, 101, 109, 116,
15: 673029, 2105431, 2692337, 4621459,
16: 38, 194, 524, 608, 647, 719, 857, 1013, 1343, 1427, 1466, 1538, 1676, 1832, 2162, 2246,
17: 31, 47, 127, 143, 223, 239, 278, 302, 319, 335, 349, 376, 415, 431, 447, 511,
18: 398, 512, 571, 989, 1633, 1747, 1806, 2224, 2868, 2982, 3041, 3459, 4103, 4217, 4276, 4694,
19: 9, 11, 29, 31, 49, 51, 69, 71, 89, 91, 109, 111, 129, 131, 149, 151,
20: 8, 13, 29, 34, 50, 55, 71, 76, 92, 97, 113, 118, 134, 139, 155, 160,
21: 23, 43, 47, 111, 131, 199, 219, 287, 307, 339, 375, 395, 463, 483, 551, 571,
22: 2253, 4946, 6694, 8417, 13408, 13868, 16101, 17849, 19572, 24563, 27256, 29004, 30727, 35718, 38411, 40159,
23: 5, 7, 17, 19, 29, 31, 41, 43, 53, 55, 65, 67, 77, 79, 83, 89,
24: 30651, 66356, 77554, 84766, 176011, 199531, 260859, 268071, 295404, 372619, 427004, 534301, 539519, 547019, 583651, 606191,
25: 79, 103, 185, 287, 311, 398, 495, 519, 584, 703, 719, 727, 911, 929, 935, 1119,
26: 221, 284, 1627, 1766, 1804, 2543, 3223, 3394, 4525, 4673, 5290, 5357, 5636, 5746, 6079, 6449,
27: 13, 15, 41, 43, 69, 71, 97, 99, 125, 127, 153, 155, 181, 183, 209, 211,
28: 4554, 8293, 13687, 18996, 27319, 31058, 36452, 41761, 50084, 53823, 59217, 64526, 72849, 76588, 81982, 87291,
29: 4, 7, 11, 19, 26, 31, 34, 35, 41, 49, 55, 56, 59, 64, 71, 79,
30: 867, 9859, 10386, 10570, 11066, 13236, 15902, 16460, 18973, 21174, 22818, 25297, 25497, 26010, 28705, 28955,
31: 239, 293, 521, 1025, 1227, 1405, 1481, 1659, 1787, 2621, 2729, 3011, 3151, 3203, 3329, 3405,
32: 10, 23, 43, 56, 76, 89, 109, 122, 124, 142, 155, 175, 188, 208, 221, 241,
[/CODE]

[CODE]
base: conjectured first 16 Riesel k
2: 509203, 762701, 777149, 790841, 992077, 1018406, 1106681, 1247173, 1254341, 1330207, 1330319, 1525402, 1554298, 1581682, 1715053, 1730653,
3: 12119, 20731, 21997, 28297, 30871, 33437, 35213, 36357, 51197, 51619, 53719, 54577, 61493, 62193, 62479, 65113,
4: 361, 919, 1114, 1444, 1486, 1681, 1849, 2326, 2419, 2629, 3301, 3676, 4456, 5014, 5209, 5539,
5: 13, 17, 37, 41, 61, 65, 85, 89, 109, 113, 133, 137, 157, 161, 181, 185,
6: 84687, 133946, 176602, 213410, 299144, 333845, 367256, 429127, 435940, 508122, 607935, 803676, 819925, 1059612, 1214450, 1250446,
7: 457, 1291, 3199, 3313, 3355, 3697, 4681, 5251, 5935, 6277, 9037, 11259, 12133, 13231, 13453, 14251,
8: 14, 112, 116, 148, 209, 307, 311, 343, 404, 502, 506, 538, 599, 658, 697, 701,
9: 41, 49, 74, 121, 129, 201, 209, 281, 289, 361, 369, 441, 449, 521, 529, 601,
10: 334, 1585, 1882, 3340, 3664, 7327, 8425, 9208, 10176, 10999, 12178, 12211, 13672, 15751, 15850, 17137,
11: 5, 7, 17, 19, 29, 31, 41, 43, 53, 55, 65, 67, 77, 79, 89, 91,
12: 376, 742, 1288, 1364, 2261, 2627, 3173, 3249, 4146, 4512, 5058, 5134, 6031, 6397, 6943, 7019,
13: 29, 41, 69, 85, 97, 101, 141, 153, 197, 209, 217, 253, 265, 302, 309, 321,
14: 4, 11, 19, 26, 34, 41, 49, 56, 64, 71, 79, 86, 94, 101, 109, 116,
15: 622403, 1346041, 2742963,
16: 100, 172, 211, 295, 625, 781, 919, 991, 1030, 1114, 1156, 1444, 1600, 1738, 1810, 1849,
17: 49, 59, 65, 86, 133, 145, 157, 161, 241, 257, 337, 353, 433, 449, 494, 521,
18: 246, 664, 723, 837, 1481, 1899, 1958, 2072, 2716, 3134, 3193, 3307, 3951, 4369, 4428, 4542,
19: 9, 11, 29, 31, 49, 51, 69, 71, 89, 91, 109, 111, 129, 131, 149, 151,
20: 8, 13, 29, 34, 50, 55, 71, 76, 92, 97, 113, 118, 134, 139, 155, 160,
21: 45, 65, 133, 153, 221, 241, 309, 329, 397, 417, 485, 489, 505, 560, 573, 593,
22: 2738, 4461, 6209, 8902, 13893, 14374, 15616, 17364, 20057, 25048, 26771, 28519, 31212, 36203, 37926, 39674,
23: 5, 7, 17, 19, 29, 31, 41, 43, 53, 55, 65, 67, 77, 79, 89, 91,
24: 32336, 69691, 109054, 124031, 135249, 140169, 177909, 196551, 213356, 215804, 217586, 326721, 335411, 360601, 386444, 406321,
25: 105, 129, 211, 313, 337, 521, 545, 729, 753, 937, 961, 1024, 1145, 1169, 1201, 1234,
26: 149, 334, 1892, 1987, 2572, 2785, 3874, 4339, 4376, 4552, 4985, 5027, 5492, 5920, 6143, 6733,
27: 13, 15, 41, 43, 69, 71, 97, 99, 125, 127, 153, 155, 173, 181, 183, 209,
28: 3769, 9078, 14472, 18211, 26534, 31843, 37237, 40976, 49299, 54608, 60002, 63741, 72064, 77373, 82767, 86506,
29: 4, 9, 11, 13, 17, 19, 21, 26, 34, 37, 41, 49, 56, 61, 64, 65,
30: 4928, 5331, 7968, 8958, 10014, 10518, 11471, 13497, 13757, 13763, 17361, 18072, 19163, 22408, 23685, 24119,
31: 145, 265, 443, 493, 519, 601, 697, 919, 1255, 1585, 2059, 2167, 2189, 2367, 2443, 2621,
32: 10, 23, 43, 56, 73, 76, 89, 109, 122, 142, 155, 175, 188, 208, 221, 241,
[/CODE]

[QUOTE=sweety439;549641]See [URL="https://github.com/xayahrainie4793/first-4-Sierpinski-Riesel-conjectures"]https://github.com/xayahrainie4793/first-4-Sierpinski-Riesel-conjectures[/URL] for the status of the 1st, 2nd, 3rd, and 4th Sierpinski/Riesel problems.

[CODE]
base: conjectured first 16 Sierpinski k
2: 78557, 157114, 271129, 271577, 314228, 322523, 327739, 482719, 542258, 543154, 575041, 603713, 628456, 645046, 655478, 903983,
3: 11047, 23789, 27221, 32549, 33141, 40247, 47969, 66869, 67747, 70381, 70667, 71367, 78283, 79141, 81241, 81663,
4: 419, 659, 794, 1466, 1676, 1769, 2246, 2414, 2609, 2636, 2651, 2981, 3176, 3734, 4514, 4889,
5: 7, 11, 31, 35, 55, 59, 79, 83, 103, 107, 127, 131, 151, 155, 175, 179,
6: 174308, 188299, 243417, 282001, 464437, 702703, 715175, 1045848, 1100966, 1128499, 1129794, 1161910, 1293662, 1434861, 1446213, 1460502,
7: 209, 1463, 3305, 3533, 3827, 5927, 7703, 9461, 9683, 10241, 10658, 10781, 12077, 12463, 12643, 14243,
8: 47, 79, 83, 181, 242, 274, 278, 376, 437, 469, 473, 571, 632, 664, 668, 766,
9: 31, 39, 111, 119, 191, 199, 271, 279, 351, 359, 431, 439, 511, 519, 591, 599,
10: 989, 1121, 3653, 3662, 8207, 9175, 9351, 9593, 9890, 10313, 11177, 11210, 12221, 13355, 14849, 16028,
11: 5, 7, 17, 19, 29, 31, 41, 43, 53, 55, 65, 67, 77, 79, 89, 91,
12: 521, 597, 1143, 1509, 2406, 2482, 3028, 3394, 4291, 4367, 4913, 5279, 6176, 6252, 6798, 7164,
13: 15, 27, 47, 71, 83, 127, 132, 139, 183, 195, 239, 251, 293, 295, 307, 351,
14: 4, 11, 19, 26, 34, 41, 49, 56, 64, 71, 79, 86, 94, 101, 109, 116,
15: 673029, 2105431, 2692337, 4621459,
16: 38, 194, 524, 608, 647, 719, 857, 1013, 1343, 1427, 1466, 1538, 1676, 1832, 2162, 2246,
17: 31, 47, 127, 143, 223, 239, 278, 302, 319, 335, 349, 376, 415, 431, 447, 511,
18: 398, 512, 571, 989, 1633, 1747, 1806, 2224, 2868, 2982, 3041, 3459, 4103, 4217, 4276, 4694,
19: 9, 11, 29, 31, 49, 51, 69, 71, 89, 91, 109, 111, 129, 131, 149, 151,
20: 8, 13, 29, 34, 50, 55, 71, 76, 92, 97, 113, 118, 134, 139, 155, 160,
21: 23, 43, 47, 111, 131, 199, 219, 287, 307, 339, 375, 395, 463, 483, 551, 571,
22: 2253, 4946, 6694, 8417, 13408, 13868, 16101, 17849, 19572, 24563, 27256, 29004, 30727, 35718, 38411, 40159,
23: 5, 7, 17, 19, 29, 31, 41, 43, 53, 55, 65, 67, 77, 79, 83, 89,
24: 30651, 66356, 77554, 84766, 176011, 199531, 260859, 268071, 295404, 372619, 427004, 534301, 539519, 547019, 583651, 606191,
25: 79, 103, 185, 287, 311, 398, 495, 519, 584, 703, 719, 727, 911, 929, 935, 1119,
26: 221, 284, 1627, 1766, 1804, 2543, 3223, 3394, 4525, 4673, 5290, 5357, 5636, 5746, 6079, 6449,
27: 13, 15, 41, 43, 69, 71, 97, 99, 125, 127, 153, 155, 181, 183, 209, 211,
28: 4554, 8293, 13687, 18996, 27319, 31058, 36452, 41761, 50084, 53823, 59217, 64526, 72849, 76588, 81982, 87291,
29: 4, 7, 11, 19, 26, 31, 34, 35, 41, 49, 55, 56, 59, 64, 71, 79,
30: 867, 9859, 10386, 10570, 11066, 13236, 15902, 16460, 18973, 21174, 22818, 25297, 25497, 26010, 28705, 28955,
31: 239, 293, 521, 1025, 1227, 1405, 1481, 1659, 1787, 2621, 2729, 3011, 3151, 3203, 3329, 3405,
32: 10, 23, 43, 56, 76, 89, 109, 122, 124, 142, 155, 175, 188, 208, 221, 241,
[/CODE]

[CODE]
base: conjectured first 16 Riesel k
2: 509203, 762701, 777149, 790841, 992077, 1018406, 1106681, 1247173, 1254341, 1330207, 1330319, 1525402, 1554298, 1581682, 1715053, 1730653,
3: 12119, 20731, 21997, 28297, 30871, 33437, 35213, 36357, 51197, 51619, 53719, 54577, 61493, 62193, 62479, 65113,
4: 361, 919, 1114, 1444, 1486, 1681, 1849, 2326, 2419, 2629, 3301, 3676, 4456, 5014, 5209, 5539,
5: 13, 17, 37, 41, 61, 65, 85, 89, 109, 113, 133, 137, 157, 161, 181, 185,
6: 84687, 133946, 176602, 213410, 299144, 333845, 367256, 429127, 435940, 508122, 607935, 803676, 819925, 1059612, 1214450, 1250446,
7: 457, 1291, 3199, 3313, 3355, 3697, 4681, 5251, 5935, 6277, 9037, 11259, 12133, 13231, 13453, 14251,
8: 14, 112, 116, 148, 209, 307, 311, 343, 404, 502, 506, 538, 599, 658, 697, 701,
9: 41, 49, 74, 121, 129, 201, 209, 281, 289, 361, 369, 441, 449, 521, 529, 601,
10: 334, 1585, 1882, 3340, 3664, 7327, 8425, 9208, 10176, 10999, 12178, 12211, 13672, 15751, 15850, 17137,
11: 5, 7, 17, 19, 29, 31, 41, 43, 53, 55, 65, 67, 77, 79, 89, 91,
12: 376, 742, 1288, 1364, 2261, 2627, 3173, 3249, 4146, 4512, 5058, 5134, 6031, 6397, 6943, 7019,
13: 29, 41, 69, 85, 97, 101, 141, 153, 197, 209, 217, 253, 265, 302, 309, 321,
14: 4, 11, 19, 26, 34, 41, 49, 56, 64, 71, 79, 86, 94, 101, 109, 116,
15: 622403, 1346041, 2742963,
16: 100, 172, 211, 295, 625, 781, 919, 991, 1030, 1114, 1156, 1444, 1600, 1738, 1810, 1849,
17: 49, 59, 65, 86, 133, 145, 157, 161, 241, 257, 337, 353, 433, 449, 494, 521,
18: 246, 664, 723, 837, 1481, 1899, 1958, 2072, 2716, 3134, 3193, 3307, 3951, 4369, 4428, 4542,
19: 9, 11, 29, 31, 49, 51, 69, 71, 89, 91, 109, 111, 129, 131, 149, 151,
20: 8, 13, 29, 34, 50, 55, 71, 76, 92, 97, 113, 118, 134, 139, 155, 160,
21: 45, 65, 133, 153, 221, 241, 309, 329, 397, 417, 485, 489, 505, 560, 573, 593,
22: 2738, 4461, 6209, 8902, 13893, 14374, 15616, 17364, 20057, 25048, 26771, 28519, 31212, 36203, 37926, 39674,
23: 5, 7, 17, 19, 29, 31, 41, 43, 53, 55, 65, 67, 77, 79, 89, 91,
24: 32336, 69691, 109054, 124031, 135249, 140169, 177909, 196551, 213356, 215804, 217586, 326721, 335411, 360601, 386444, 406321,
25: 105, 129, 211, 313, 337, 521, 545, 729, 753, 937, 961, 1024, 1145, 1169, 1201, 1234,
26: 149, 334, 1892, 1987, 2572, 2785, 3874, 4339, 4376, 4552, 4985, 5027, 5492, 5920, 6143, 6733,
27: 13, 15, 41, 43, 69, 71, 97, 99, 125, 127, 153, 155, 173, 181, 183, 209,
28: 3769, 9078, 14472, 18211, 26534, 31843, 37237, 40976, 49299, 54608, 60002, 63741, 72064, 77373, 82767, 86506,
29: 4, 9, 11, 13, 17, 19, 21, 26, 34, 37, 41, 49, 56, 61, 64, 65,
30: 4928, 5331, 7968, 8958, 10014, 10518, 11471, 13497, 13757, 13763, 17361, 18072, 19163, 22408, 23685, 24119,
31: 145, 265, 443, 493, 519, 601, 697, 919, 1255, 1585, 2059, 2167, 2189, 2367, 2443, 2621,
32: 10, 23, 43, 56, 73, 76, 89, 109, 122, 142, 155, 175, 188, 208, 221, 241,
[/CODE][/QUOTE]

Remain k's: (less than the 4th CK) (at n=3000)

R4: 1159, 1189
R5: (none)
R7: (31 k's)
R8: (none)
R9: (none)
R10: 2452
R11: (none)
R12: 1132
R13: (none)
R14: (none)
R16: (none)
R17: (none)
R18: 533, 597
R19: (none)
R20: (none)
R21: (none)
R23: (none)
R25: 181, 235
R26: (41 k's)
R27: (none)
R29: (none)
R31: (20 k's)
R32: 29
R33: 257, 339, 817, 851, 951, 1123, 1240
R34: (none)
R35: (none)
R37: 33, 81, 149
R38: 44
R39: (none)
R41: (none)
R43: 13, 55
R44: (none)
R45: 197, 257
R47: (none)
R49: 82
R50: 37, 68
R51: (none)
R53: (none)
R54: 45
R55: (none)
R56: 43
R57: 281
R59: (none)
R61: 37, 53, 100, 139, 165, 229, 313, 353, 365, 389, 421
R62: 22, 26
R64: (none)
R128: 46
R256: 191, 261, 286

S4: 1238, 1286
S5: (none)
S7: (34 k's)
S8: (none)
S9: (none)
S10: 100, 269, (1000), 1343, 2573, (2690)
S11: (none)
S12: 12, (144), 885, 911, 976, 1041, 1433, 1468
S13: (none)
S14: (none)
S16: 89
S17: 53
S18: 18, (324), 607, 761, 873, 922, 983
S19: (none)
S20: (none)
S21: (none)
S23: (none)
S25: 71, 181, 222
S26: (39 k's)
S27: 33
S29: (none)
S31: (45 k's)
S32: 4, 16
S33: 67, 203, 1207, 1317, 1439, 1531, 1563, 1597
S34: (none)
S35: (none)
S37: 37, 63, 94, 127, 134, 171
S38: 1, (38)
S39: (none)
S41: (none)
S43: 37, 56
S44: (none)
S45: 139, 217
S47: (none)
S49: (none)
S50: 1, (50)
S51: 38
S53: 4, 17, 19
S54: (none)
S55: 1, 36
S56: 46
S57: 117, 207
S59: (none)
S61: 119, 127, 155, 164, 230, 249, 262, 324, 340, 342, 353, 359, 368
S62: 1, 27
S64: (none)
S128: 16, 40, 47, 83, 88, 94, 122
S256: 89, 116, 215, 230, 281, 329, 383, 398, 407, 434, 459, 504

(k's with "()" are the k's excluded from testing (these k's are still included in the conjectures), i.e. k's that are multiples of base (b) and where (k+-1)/gcd(k+-1,b-1) (+ for Sierpinski, - for Riesel) is not prime)

[QUOTE=sweety439;549642]Remain k's: (less than the 4th CK) (at n=3000)

R4: 1159, 1189
R5: (none)
R7: (31 k's)
R8: (none)
R9: (none)
R10: 2452
R11: (none)
R12: 1132
R13: (none)
R14: (none)
R16: (none)
R17: (none)
R18: 533, 597
R19: (none)
R20: (none)
R21: (none)
R23: (none)
R25: 181, 235
R26: (41 k's)
R27: (none)
R29: (none)
R31: (20 k's)
R32: 29
R33: 257, 339, 817, 851, 951, 1123, 1240
R34: (none)
R35: (none)
R37: 33, 81, 149
R38: 44
R39: (none)
R41: (none)
R43: 13, 55
R44: (none)
R45: 197, 257
R47: (none)
R49: 82
R50: 37, 68
R51: (none)
R53: (none)
R54: 45
R55: (none)
R56: 43
R57: 281
R59: (none)
R61: 37, 53, 100, 139, 165, 229, 313, 353, 365, 389, 421
R62: 22, 26
R64: (none)
R128: 46
R256: 191, 261, 286

S4: 1238, 1286
S5: (none)
S7: (34 k's)
S8: (none)
S9: (none)
S10: 100, 269, (1000), 1343, 2573, (2690)
S11: (none)
S12: 12, (144), 885, 911, 976, 1041, 1433, 1468
S13: (none)
S14: (none)
S16: 89
S17: 53
S18: 18, (324), 607, 761, 873, 922, 983
S19: (none)
S20: (none)
S21: (none)
S23: (none)
S25: 71, 181, 222
S26: (39 k's)
S27: 33
S29: (none)
S31: (45 k's)
S32: 4, 16
S33: 67, 203, 1207, 1317, 1439, 1531, 1563, 1597
S34: (none)
S35: (none)
S37: 37, 63, 94, 127, 134, 171
S38: 1, (38)
S39: (none)
S41: (none)
S43: 37, 56
S44: (none)
S45: 139, 217
S47: (none)
S49: (none)
S50: 1, (50)
S51: 38
S53: 4, 17, 19
S54: (none)
S55: 1, 36
S56: 46
S57: 117, 207
S59: (none)
S61: 119, 127, 155, 164, 230, 249, 262, 324, 340, 342, 353, 359, 368
S62: 1, 27
S64: (none)
S128: 16, 40, 47, 83, 88, 94, 122
S256: 89, 116, 215, 230, 281, 329, 383, 398, 407, 434, 459, 504[/QUOTE]

Reserve some 1k bases (S17, S27, S51, S56, R38, R54)