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

Nov 2016

2,819 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 2,819 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

54038 Posts

Update pdf files for the Sierpinski/Riesel conjectures
Attached Files
 Sierpinski problems.pdf (365.2 KB, 25 views) Riesel problems.pdf (386.1 KB, 26 views)

Last fiddled with by sweety439 on 2021-02-15 at 16:00

2020-12-28, 02:00   #1181
sweety439

Nov 2016

2,819 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, 65 views)

 2020-12-29, 12:11 #1182 sweety439   Nov 2016 54038 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 1011010010102 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

281910 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

 2021-02-24, 18:20 #1185 sweety439   Nov 2016 2,819 Posts Update the status of Riesel problems to include the new primes for R2 and new test limits for R2, R6 (k=1597), R108 (k = 5351, 6528, 13162) Last fiddled with by sweety439 on 2021-02-24 at 18:31
 2021-02-24, 18:29 #1186 sweety439   Nov 2016 2,819 Posts Update the status of Sierpinski problems to include the new primes for S80 (all k except k=947), S81, S108 (k=20543) and the new test limits for S2, S80 (all k except k=947), S81, S97 Last fiddled with by sweety439 on 2021-02-24 at 18:32
2021-02-24, 18:36   #1187
sweety439

Nov 2016

B0316 Posts

Upload pdf files for these conjectures

Also listed for 2<=b<=128 and 1<=k<=128: Riesel Sierpinski
Attached Files
 Riesel problems.pdf (394.7 KB, 28 views) Sierpinski problems.pdf (365.1 KB, 36 views)

Last fiddled with by sweety439 on 2021-04-15 at 06:35

2021-02-24, 23:55   #1188
sweety439

Nov 2016

2,819 Posts
Riesel base 162

Quote:
 Originally Posted by sweety439 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
searched to n=2000, see the text file for the status, 0 if no (probable) prime found for this k

CK=3259

Only list k == 1 mod 7 and k == 1 mod 23 since other k are already in CRUS
Attached Files
 R162 status.txt (4.6 KB, 22 views)

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