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2020-07-31, 05:26   #122
sweety439

Nov 2016

23×97 Posts

Quote:
 Originally Posted by sweety439 Update the status file for: SR8, R9: k<=1024 S12: k<=1143 (the 3rd CK) R12: k<=1288 (the 3rd CK) SR8 skipped the cube k's and the k's having covering set {3, 5, 13} (i.e. for S8, k == 47, 79, 83, 181 mod 195; for R8, k == 14, 112, 116, 148 mod 195) SR9 skipped the square k's and the k's having covering set {2, 5} (i.e. k == 41, 49 mod 80) (this is for (k*b^n+-1)/gcd(k+-1,b-1), however, you can ignore the k's such that gcd(k+-1,b-1) is not 1, e.g. for S8, you can ignore the k's == 6 mod 7)
Remain k's:

S8: 256 (GFN, at n=(2^33-8)/3-1), 370 (extended, corresponding number should be divided by 7 to get a prime since 370*8^n+1 has trivial factor of 7, at n=10K), 467 (at n=833333 due to http://www.prothsearch.com/riesel1a.html)

R8: 239 (extended, corresponding number should be divided by 7 to get a prime since 239*8^n-1 has trivial factor of 7, at n=10K), 247 (at n=76666 due to http://www.prothsearch.com/riesel2.html), 757 (extended, corresponding number should be divided by 7 to get a prime since 757*8^n-1 has trivial factor of 7, at n=10K)

R9: 386, 744 (both at n=25K)

S12: 12 (GFN, at n=2^25-2), 885, 911, 976, 1041 (all k except k=12 at n=25K)

R12: 1132 (at n=21760)

2020-08-06, 08:28   #123
sweety439

Nov 2016

23×97 Posts

These are the status for the first 4 conjectures for SR32 and SR128 (I only update the power-of-2 bases here, since they are more interesting, for more SR bases, see the files in post https://mersenneforum.org/showpost.p...&postcount=930 and the GitHub page https://github.com/xayahrainie4793/f...el-conjectures)

Code:
base   CK               remain k
S32    10, 23, 43, 56   4, 16 (proven if GFN are excluded)
R32    10, 23, 43, 56   29 (at n=2M by CRUS search for R1024)
S128   44, 85, 98, 173  16, 40, 47, 83, 88, 94, 122
R128   44, 59, 85, 86   46
Attached Files
 S32.txt (382 Bytes, 5 views) R32.txt (382 Bytes, 5 views) S128.txt (1.2 KB, 7 views) R128.txt (589 Bytes, 5 views)

Last fiddled with by sweety439 on 2020-08-06 at 08:32

2020-08-06, 16:09   #124
henryzz
Just call me Henry

"David"
Sep 2007
Cambridge (GMT/BST)

2·2,861 Posts

Quote:
 Originally Posted by sweety439 These are the status for the first 4 conjectures for SR32 and SR128 (I only update the power-of-2 bases here, since they are more interesting, for more SR bases, see the files in post https://mersenneforum.org/showpost.p...&postcount=930 and the GitHub page https://github.com/xayahrainie4793/f...el-conjectures) Code: base CK remain k S32 10, 23, 43, 56 4, 16 (proven if GFN are excluded) R32 10, 23, 43, 56 29 (at n=2M by CRUS search for R1024) S128 44, 85, 98, 173 16, 40, 47, 83, 88, 94, 122 R128 44, 59, 85, 86 46
Testing limits might be useful in your files. I assume you have checked for base 2 primes on https://www.rieselprime.de/default.htm

2020-08-07, 15:47   #125
sweety439

Nov 2016

23×97 Posts

Quote:
 Originally Posted by henryzz Testing limits might be useful in your files. I assume you have checked for base 2 primes on https://www.rieselprime.de/default.htm
OK, but see the GitHub page https://github.com/xayahrainie4793/f...el-conjectures, there are too many "NA" in these files, however I an give you the test limit for some bases:

e.g.

S4 for all k: 10K
S7 for all k: 3K
R7 for k == 1 mod 6: 3K
R7 for other k: 15K (given using page https://www.rose-hulman.edu/~rickert/Compositeseq/)
S10 for k = 100: 2^31-3
S10 for k = 269: 100K
S12 for k = 12: 2^25-2
S12 for other k: 25K
R12 (only one k remain: 1132): 21760
S25 for k = 71 and k = 181: 10K
S25 for k = 222: 350K (given by CRUS)
SR26 for all k: 2K

Last fiddled with by sweety439 on 2020-08-07 at 15:47

 2020-08-07, 15:52 #126 sweety439     Nov 2016 23×97 Posts There are pages shown the status (including the test limit) for the conjectures of (k*b^n+-1)/gcd(k+-1,b-1) (+ for Sierpinski, - for Riesel) with bases 2<=b<=128 and b=256, 512, 1024 Sierpinski conjectures Riesel conjectures Edit: the test limit for S10 k=100 is now 2^31-3 (2.147G), see http://www.prothsearch.com/GFN10.html Last fiddled with by sweety439 on 2020-08-07 at 15:54
2020-08-08, 15:52   #127
sweety439

Nov 2016

23·97 Posts

Quote:
 Originally Posted by sweety439 Remain k's: S8: 256 (GFN, at n=(2^33-8)/3-1), 370 (extended, corresponding number should be divided by 7 to get a prime since 370*8^n+1 has trivial factor of 7, at n=10K), 467 (at n=833333 due to http://www.prothsearch.com/riesel1a.html) R8: 239 (extended, corresponding number should be divided by 7 to get a prime since 239*8^n-1 has trivial factor of 7, at n=10K), 247 (at n=76666 due to http://www.prothsearch.com/riesel2.html), 757 (extended, corresponding number should be divided by 7 to get a prime since 757*8^n-1 has trivial factor of 7, at n=10K) R9: 386, 744 (both at n=25K) S12: 12 (GFN, at n=2^25-2), 885, 911, 976, 1041 (all k except k=12 at n=25K) R12: 1132 (at n=21760)
(370*8^8300+1)/gcd(370+1,8-1) is (probable) prime

Update the correct file for S8 k<=1024
Attached Files
 S8.txt (7.0 KB, 5 views)

Last fiddled with by sweety439 on 2020-08-08 at 15:56

 2020-08-18, 17:24 #128 sweety439     Nov 2016 223110 Posts https://github.com/xayahrainie4793/all-k-1024 All k<=1024 for all bases 2<=b<=32 and b=64, 256, searched up to n=4096 Last fiddled with by sweety439 on 2020-08-18 at 17:34

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