Bases > 1030 and k's > CK

[sweety439]

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)

[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)

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

[henryzz]

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)

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

[sweety439]

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

[sweety439]

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

[sweety439]

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

[sweety439]

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

[sweety439]

Riesel base 2021, CK = 338, tested to n=2000

checked k=32, where n == 0 mod 5 is algebraic, k=32 does not make a full covering set with partial algebra factors

[VBCurtis]

Sweety-
You have been threatened with a ban from this forum for posting useless trivia (among many other annoying behaviors).
"useless trivia", as one example: Work that can be computed so quickly that anyone else who cares about the work can do it so quickly themselves that they should not trust your work.

You tested a base with a conjecture of 338 to n=2000? That took what, 3 minutes? It may have taken as long to type the commands to invoke the programs as it did to compute. That's the very definition of useless content. This is why Gary has asked you to no longer post on CRUS.

If you continue to post (a) useless information or (b) on subfora where you have been asked to not post, you risk a ban. A concrete measure you can use: if you can compute the information in less than a CPU-week, you should not post it.

You've used up your good grace from others with your tiny corrections of e.g. search limits or typos. Those posts aren't welcome either. You have a personal choice to make- stop posting noise, or lose your posting privileges. 95% of your posts waste the reader's time, and the mods are tired of having their time wasted by you.
It's time to change your behavior.

[NHoodMath]

Originally Posted by sweety439

Riesel base 2021, CK = 338, tested to n=2000

checked k=32, where n == 0 mod 5 is algebraic, k=32 does not make a full covering set with partial algebra factors

I already had this one (R2021) searched to 13K, going to 25K rn (BTW I did finish those 3 k's on S2020 to n=100K, no primes)

[Uncwilly]

Originally Posted by VBCurtis

Sweety-
You have been threatened with a ban from this forum for posting useless trivia (among many other annoying behaviors).

Another behaviour that is not welcome: going out of your way to find numbers/sequences in base 36 that make naughty words.