20200725, 20:01  #914 
Nov 2016
100110100101_{2} Posts 
Done to base 2500

20200726, 15:34  #915 
Nov 2016
3×823 Posts 
Some CK in the text files in post #772have been fixed:
S970: 139823 > 134552 (k = 134552 has covering set {3, 7, 44851}) S1150: >1M > 755222 (k = 755222 has covering set {3, 7, 63031}) S1876: >1M > 473969 (k = 473969 has covering set {3, 37, 31723}) R1150: >1M > 190243 (k = 190243 has covering set {3, 7, 63031}) R1414: 64 > 284 (k = 64 is unlikely to have a covering set, this error is because for this k, all n <= 1000 has a prime factor <= 10000) R1876: 793972 > 475846 (k = 475846 has covering set {3, 37, 31723}) The text file in post #772 have these errors is because I only tested the primes <= 10000 and the exponents <= 1000, but all these covering sets of these k has a prime > 10000, now I tested the primes <= 100000 and the exponents <= 2100, the fixed files are in the post #914 Last fiddled with by sweety439 on 20200726 at 15:41 
20200726, 15:36  #916 
Nov 2016
100110100101_{2} Posts 
See https://github.com/xayahrainie4793/E...f9596b6ce34d02 (Sierpinski) and https://github.com/xayahrainie4793/E...18a8665bfad2d0 (Riesel) for the updating.

20200726, 15:55  #917 
Nov 2016
3×823 Posts 
Reserve: (for k's > CK)
S4: k = 1238 & 1286 R4: k = 1159 & 1189 
20200726, 15:59  #918 
Nov 2016
3×823 Posts 
See https://github.com/xayahrainie4793/f...elconjectures for the status of the first 4 CK for the Sierpinski/Riesel conjectures for the bases b<=64 with smaller CK

20200726, 16:12  #919 
Nov 2016
3·823 Posts 

20200726, 16:43  #920  
Nov 2016
3·823 Posts 
Quote:
A078680: S2, k = index A040076: S2, k = index (allow n=0) A050412: R2, k = index + 1 A040081: R2, k = index (allow n=0) A291437: S3, k = index * 2 (allow n=0) A177330: R4, k = prime(index) if prime(index) == 1 mod 3, n = value/2; k = 2*prime(index) if prime(index) == 2 mod 3, n = (value1)/2 A250204: S6, k = index, k != 4 mod 5 A250205: R6, k = index, k != 1 mod 5 A217377: R6, k = index * 5 + 1 (allow n=0) A069568: R10, k = index * 9 + 1 A083747: R10, k = index * 9 + 1 (allow n=0) A090584: R10, k = index * 3 + 1, k != 1 mod 9 (allow n=0) A090465: R10, k = index + 1, k != 1 mod 3 (allow n=0) A257459: R10, k = prime(index) * 9 + 1 A232210: R10, k = prime(index) * 3 + 1, k != 1 mod 9 A257461: R10, k = prime(index) + 1, k != 1 mod 3 

20200728, 12:54  #921 
Nov 2016
3×823 Posts 
Update all primes for R102 and some primes for S80

20200730, 14:54  #922 
Nov 2016
3·823 Posts 
Extended Sierpinski problem base b:
Finding and proving the smallest k>=1 such that (k*b^n+1)/gcd(k+1,b1) is not prime for all integers n>=1. (kvalues that make a full covering set with all or partial algebraic factors are excluded from the conjectures) Extended Riesel problem base b: Finding and proving the smallest k>=1 such that (k*b^n1)/gcd(k1,b1) is not prime for all integers n>=1. (kvalues that make a full covering set with all or partial algebraic factors are excluded from the conjectures) 
20200731, 05:12  #923 
Nov 2016
3×823 Posts 
The reason for why S8 k=27, S16 k=4, R4 k=1, R8 k=1, R16 k=1, R27 k=1, R36 k=1 are excluded from the conjectures is the same as the reason for why in CRUS conjectures, R12 k=1, R14 k=1, R18 k=1, R20 k=1, R24 k=1 are excluded from the conjectures
The reason is although they have a prime, but they can have only this prime, thus excluded from the conjectures, a kvalue with no covering set is included from the conjectures if and only if this kvalue may have infinitely many primes Last fiddled with by sweety439 on 20200806 at 06:44 
20200803, 23:47  #924  
Nov 2016
3×823 Posts 
Quote:
Bases 235, 748, 1261, 1774, 2287, 2800, 3313, 3826, 4339, 4852, 5365, 5878, 6391, 6904, 7417, 7930, 8443, 8956, 9469, 9982, ...: n == 1 mod 3: factor of 3, n == 2 mod 3: factor of 19 Bases 397, 1396, 2395, 3394, 4393, 5392, 6391, 7390, 8389, 9388, ...: n == 1 mod 3: factor of 3, n == 5 mod 6: factor of 37 Bases 721, 2692, 4663, 6634, 8605, ...: n == 1 mod 3: factor of 3, n == 2 mod 3: factor of 73 Bases 1045, 3988, 6931, 9874, ...: n == 1 mod 3: factor of 3, n == 5 mod 6: factor of 109 Bases 334, 847, 1360, 1873, 2386, 2899, 3412, 3925, 4438, 4951, 5464, 5977, 6490, 7003, 7516, 8029, 8542, 9055, 9568, ...: n == 1 mod 3: factor of 19, n == 2 mod 3: factor of 3 Bases 307, 1306, 2305, 3304, 4303, 5302, 6301, 7300, 8299, 9298, ...: n == 1 mod 6: factor of 37, n == 2 mod 3: factor of 3 Bases 1468, 3439, 5410, 7381, 9352, ...: n == 1 mod 3: factor of 73, n == 2 mod 3: factor of 3 Bases 2008, 4951, 7894, ...: n == 1 mod 6: factor of 109, n == 2 mod 3: factor of 3 

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