mersenneforum.org A Sierpinski/Riesel-like problem
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2020-12-23, 19:13   #1178
sweety439

Nov 2016

22·691 Posts

Quote:
 Originally Posted by sweety439 (20543*108^3375+1)/107 is prime 3 k's for R108 are still remain ....
Still no prime found for these 3 k's, they are likely tested to n>=6000

Also see post #341 for the primes at n=1K=2K for S/R 108

 2020-12-23, 21:46 #1179 sweety439   Nov 2016 22×691 Posts We can use the sense of http://www.iakovlev.org/zip/riesel2.pdf to conclude that (k*b^n+c)/gcd(k+c,b-1) (k>=1, b>=2, c != 0, gcd(k,c) = 1, gcd(b,c) = 1) eventually should yield a prime, when it does not have primes for small n>=1 We should find the n's such that (k*b^n+c)/gcd(k+c,b-1) does not have small prime factors (and the znorder of b mod its prime factors are also not small), nor has algebra factors (i.e. k*b^n and -c are both rth powers for some r>1, or k*b^n*c is of the form 4*m^4) Last fiddled with by sweety439 on 2020-12-23 at 21:52
2020-12-27, 19:47   #1180
sweety439

Nov 2016

22·691 Posts

Update pdf files for the Sierpinski/Riesel conjectures
Attached Files
 Sierpinski problems.pdf (247.3 KB, 19 views) Riesel problems.pdf (265.5 KB, 21 views)

2020-12-28, 02:00   #1181
sweety439

Nov 2016

276410 Posts

Quote:
 Originally Posted by sweety439 Update current status file for R/S 40
Update newest status text file for R/S 40
Attached Files
 pfgw.log (15.8 KB, 12 views)

 2020-12-29, 12:11 #1182 sweety439   Nov 2016 22·691 Posts Riesel base 2021 is proven!!! With CK=13, see https://github.com/xayahrainie4793/E...0to%202048.txt Code: k,n 1,67 2,1048 3,1773 4,3 5,140 6,2 7,117 8,2 9,1 10,269 11,14 12,1 Interestingly, the prime for k=2 and k=3 are both large.
 2020-12-29, 14:44 #1183 kar_bon     Mar 2006 Germany 2×1,433 Posts So you got your own definition of GCD? In the first post reads (for Riesel side): (k*b^n-1)/gcd(k-1, b-1) b=2021, k=1, n=67 (from table above) GCD for k=1 in the above formula is undefined and so (1*2021^67-1)/2020 is prime but do not correlates to your definiton of the problem and the definition of GCD.
2020-12-30, 01:27   #1184
sweety439

Nov 2016

22×691 Posts

Quote:
 Originally Posted by kar_bon So you got your own definition of GCD? In the first post reads (for Riesel side): (k*b^n-1)/gcd(k-1, b-1) b=2021, k=1, n=67 (from table above) GCD for k=1 in the above formula is undefined and so (1*2021^67-1)/2020 is prime but do not correlates to your definiton of the problem and the definition of GCD.
See https://en.wikipedia.org/wiki/Greatest_common_divisor, gcd(a, 0) = |a|, for a ≠ 0, since any number is a divisor of 0, and the greatest divisor of a is |a|. This is usually used as the base case in the Euclidean algorithm. The GCD is 2020 for all k == 1 mod 2020, including k = 1

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