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 2020-12-21, 22:21 #1134 sweety439   Nov 2016 22·3·5·47 Posts Riesel base 137 Code: 1,11 2,2 3,27 4,1 5,12 6,1 7,1 8,2 9,(partial algebra factors) 10,5 11,0 12,2 13,0 14,4 15,0 16,231 With CK=17 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*137^q - 1) * (m*137^q + 1) odd n: factor of 2 This includes k = 9 k = 11, 13, 15 remain at n=2000 Last fiddled with by sweety439 on 2021-02-25 at 22:38
 2020-12-21, 22:24 #1135 sweety439   Nov 2016 22·3·5·47 Posts Riesel base 138 Code: 1,2 138,1 275,1 412,2 549,4 686,1 823,1 960,1 1097,6 1234,28 1371,1 1508,2 1645,1 1782,2 With CK=1806 Only list k == 1 mod 137 since other k are already in CRUS no remain k with k == 1 mod 137, totally list of the remain k is {408, 688, 831, 1074, 1743}, all remain at n=300K, see CRUS Last fiddled with by sweety439 on 2021-02-27 at 06:57
 2020-12-21, 22:25 #1136 sweety439   Nov 2016 22×3×5×47 Posts Riesel base 139 Code: 1,163 2,1 3,114 4,(partial algebra factors) 5,1 With CK=6 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*139^q - 1) * (m*139^q + 1) odd n: factor of 5 This includes k = 4 Conjecture proven
 2020-12-21, 22:26 #1137 sweety439   Nov 2016 1011000001002 Posts Riesel base 140 Code: 1,79 2,2 3,1 4,5 5,30 6,1 7,7 8,2 9,1 10,1 11,108 12,2 13,7 14,16 15,1 16,1 17,8 18,6 19,1 20,2 21,1 22,1 23,2 24,1 25,1 26,4 27,1 28,1 29,18 30,2 31,1 32,16 33,12 34,1 35,6 36,1 37,1 38,448 39,2 40,9 41,8 42,1 43,3 44,2 45,1 With CK=46 Conjecture proven
 2020-12-21, 23:59 #1138 sweety439   Nov 2016 22·3·5·47 Posts A (Sierpinski/Riesel) base b has 2-cover if and only if b+1 is not prime or prime power
 2020-12-22, 00:00 #1139 sweety439   Nov 2016 282010 Posts The formula for Sierpinski conjectures in CRUS is k*b^n+1 The formula for Riesel conjectures in CRUS is k*b^n-1 The formula for Sierpinski conjectures in this project is (k*b^n+1)/gcd(k+1,b-1) The formula for Riesel conjectures in this project is (k*b^n-1)/gcd(k-1,b-1)
 2020-12-22, 00:03 #1140 sweety439   Nov 2016 22·3·5·47 Posts The reason for (k=27 is excluded from S8 in this project) (k=4 is excluded from S16 in this project) (k=1 is excluded from R4 in this project) (k=1 is excluded from R8 in this project) (k=1 is excluded from R16 in this project) (k=1 is excluded from R36 in this project) (k=1 is excluded from R100 in this project) (k=1 is excluded from R128 in this project) is the same as (k=1 is excluded from R14 in CRUS) (k=1 is excluded from R18 in CRUS) (k=1 is excluded from R20 in CRUS) (k=1 is excluded from R24 in CRUS) (k=1 is excluded from R30 in CRUS) (k=1 is excluded from R32 in CRUS) (k=1 is excluded from R38 in CRUS) (k=1 is excluded from R42 in CRUS)
2020-12-22, 00:05   #1141
sweety439

Nov 2016

22·3·5·47 Posts
Riesel base 141

searched to n=2000, see the text file for the status, 0 if no (probable) prime found for this k

CK=285

Only k = 201 remain at n=2000
Attached Files
 R141 status.txt (1.9 KB, 18 views)

Last fiddled with by sweety439 on 2020-12-22 at 00:19

 2020-12-22, 00:13 #1142 sweety439   Nov 2016 22×3×5×47 Posts Riesel base 142 Code: 1,1231 2,1 3,26 4,3 5,1 6,3 7,1 8,7 9,1 10,2 11,14 With CK=12 Conjecture proven
 2020-12-22, 00:14 #1143 sweety439   Nov 2016 22·3·5·47 Posts Riesel base 143 Code: 1,3 2,2 3,16 4,1 With CK=5 Conjecture proven
 2020-12-22, 00:17 #1144 sweety439   Nov 2016 22×3×5×47 Posts Riesel base 144 Code: 1,(full algebra factors) 2,24 3,1 4,(full algebra factors) 5,1 6,1 7,5 8,1 9,(full algebra factors) 10,1 11,1 12,1 13,1 14,4 15,10 16,(full algebra factors) 17,1 18,1 19,4 20,1 21,1 22,1 23,134 24,2 25,(full algebra factors) 26,5 27,2 28,2 29,4 30,519 31,1 32,3 33,1 34,8 35,1 36,(full algebra factors) 37,3 38,1 39,964 40,1 41,1 42,1 43,2 44,6 45,3 46,97 47,2 48,1 49,(full algebra factors) 50,2 51,3 52,1 53,1 54,8 55,1 56,1 57,20 58,35 With CK=59 All k = m^2 for all n; factors to: (m*12^n - 1) * (m*12^n + 1) This includes k = 1, 4, 9, 16, 25, 36, 49 Conjecture proven

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