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 2020-12-22, 18:04 #1156 sweety439   Nov 2016 2,819 Posts Riesel base 152 Code: 1,270217 2,796 3,3 4,1 5,12 6,1 7,1 8,2 9,1 10,5 11,14 12,1 13,23 14,343720 15,2 With CK=16 k=1 prime given by generalized repunit prime search, k=14 prime given by CRUS Conjecture proven Last fiddled with by sweety439 on 2021-02-11 at 05:23
 2020-12-22, 18:13 #1157 sweety439   Nov 2016 1011000000112 Posts Riesel base 153 Code: 1,3 2,2 3,1 4,3 5,1 6,2 7,2 8,1 9,(partial algebra factors) 10,2 11,2 12,21659 13,2 14,1 15,5 16,1 17,(partial algebra factors) 18,1 19,1 20,4 21,70 22,23 23,1 24,1 25,(partial algebra factors) 26,2 27,44 28,1 29,1 30,2 31,1 32,8 33,1 With CK=34 k=12 prime given by CRUS (Condition 1): All k where k = m^2 and m = = 3 or 5 mod 8: for even n let k = m^2 and let n = 2*q; factors to: (m*153^q - 1) * (m*153^q + 1) odd n: factor of 2 This includes k = 9, 25 (Condition 2): All k where k = 17*m^2 and m = = 1 or 7 mod 8: even n: factor of 2 for odd n let k = 17*m^2 and let n=2*q-1; factors to: [m*3^(2q-1)*17^q - 1] * [m*3^(2q-1)*17^q + 1] This includes k = 17 Conjecture proven Last fiddled with by sweety439 on 2021-02-11 at 05:28
 2020-12-22, 18:18 #1158 sweety439   Nov 2016 2,819 Posts For the list of the CK, see https://github.com/xayahrainie4793/E...0to%202048.txt (Riesel) and https://github.com/xayahrainie4793/E...0to%202048.txt (Sierpinski)
 2020-12-22, 19:09 #1159 sweety439   Nov 2016 2,819 Posts Riesel base 154 Code: 1,5 2,1 3,1 4,(partial algebra factors) 5,1 6,1989 7,1 8,1 9,(partial algebra factors) 10,3 11,1 12,1 13,2 14,78 15,1 16,1 17,1 18,1 19,324 20,1 21,7 22,1 23,1 24,106 25,1 26,1 27,1 28,1 29,62 30,2 31,7 32,3 33,1 34,2 35,1 36,7 37,2 38,1 39,326 40,1 41,3 42,3 43,1 44,6 45,3 46,1 47,1 48,2 49,(partial algebra factors) 50,1 51,1 52,1 53,1 54,30 55,1 56,1 57,3 58,5 59,6 60,1 With CK=61 All k where k = m^2 and m = = 2 or 3 mod 5: for even n let k = m^2 and let n = 2*q; factors to: (m*154^q - 1) * (m*154^q + 1) odd n: factor of 5 This includes k = 4, 9, 49 Conjecture proven
 2020-12-22, 19:11 #1160 sweety439   Nov 2016 2,819 Posts Riesel base 155 Code: 1,3 2,2 3,2 4,1 With CK=5 Conjecture proven
 2020-12-22, 19:12 #1161 sweety439   Nov 2016 2,819 Posts Riesel base 156 Even the CK is unknown, it is only known that CK is >5M and <= 2113322677, and the CK equals 2113322677 if CK is neither == 1 mod 5 nor == 1 mod 31 (see CRUS condensed table) (Condition 1): All k where k = m^2 and m = = 28 or 129 mod 157: for even n let k = m^2 and let n = 2*q; factors to: (m*156^q - 1) * (m*156^q + 1) odd n: factor of 157 (Condition 2): All k where k = 39*m^2 and m = = 56 or 101 mod 157: even n: factor of 157 for odd n let k = 39*m^2 and let n=2*q-1; factors to: [m*2^(2*q-1)*39^q - 1] * [m*2^(2*q-1)*39^q + 1] Last fiddled with by sweety439 on 2021-02-11 at 05:31
 2020-12-22, 19:13 #1162 sweety439   Nov 2016 2,819 Posts Riesel base 157 Code: 1,17 2,1 3,2 4,45 5,4 6,1 7,32 8,56 9,1 10,1 11,1 12,2 13,10 14,7 15,49 16,5 With CK=17 Conjecture proven
 2020-12-22, 19:16 #1163 sweety439   Nov 2016 2,819 Posts Riesel base 158 Code: 1,7 2,2 3,2 4,1 5,2 6,1 7,39 8,20 9,35 10,1 11,18 12,2 13,1 14,4 15,17 16,17 17,14 18,1 19,1 20,34 21,2 22,7 23,6 24,9 25,19 26,2 27,19 28,1 29,0 30,9 31,9 32,4 33,5 34,5223 35,2 36,5 37,15 38,74 39,49 40,5 41,94 42,3 43,1 44,0 45,1 46,147 47,273942 48,1 49,1 50,2 51,3 With CK=52 k = 34, 47 primes given by CRUS k = 29, 44 remain at n=300K by CRUS Last fiddled with by sweety439 on 2021-02-25 at 22:37
 2020-12-22, 19:18 #1164 sweety439   Nov 2016 2,819 Posts Riesel base 159 Code: 1,13 2,1 3,2160 4,(partial algebra factors) 5,1 6,1 7,6 8,22 With CK=9 k=3 prime found by the project for k<=12 and bases <= 1024 All k where k = m^2 and m = = 2 or 3 mod 5: for even n let k = m^2 and let n = 2*q; factors to: (m*159^q - 1) * (m*159^q + 1) odd n: factor of 5 This includes k = 4 Conjecture proven Last fiddled with by sweety439 on 2020-12-23 at 00:29
 2020-12-22, 19:19 #1165 sweety439   Nov 2016 B0316 Posts Riesel base 160 Code: 1,7 2,2 3,1 4,3 5,3 6,8 7,1 8,1 9,1 10,2 11,1 12,11 13,2 14,1 15,1 16,1 17,1 18,1 19,1 20,7570 21,1 With CK=22 k=20 prime given by CRUS Conjecture proven Last fiddled with by sweety439 on 2021-02-11 at 05:24
 2020-12-22, 19:20 #1166 sweety439   Nov 2016 2,819 Posts Riesel base 161 Code: 1,3 2,228 3,1 4,1 5,2 6,1 7,1 8,2 9,1 10,1 11,2 12,1 13,1 14,10 15,3 16,3 17,2 18,1 19,3 20,26 21,4 22,1 23,4 24,1 25,1 26,2 27,2 28,1 29,2 30,8 31,1 32,316 33,2 34,11 35,2 36,15 37,1 38,4 39,2 40,67 41,14 42,1 43,1 44,4 45,1 46,1 47,2 48,1 49,103 50,328 51,1 52,549 53,46 54,1 55,153 56,4 57,2 58,1 59,36 60,2 61,1 62,4 63,3 64,1 With CK=65 Conjecture proven

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