A Sierpinski/Riesel-like problem

[sweety439]

Reserve SR6 to n=100K, this is the sieve file. (include all remain k = 4 mod 5 for S6 and all remain k = 1 mod 5 for R6, all these k are at n=25K) (please see this file for the remain k for SR6 at n=25K which is not in CRUS)

[sweety439]

Originally Posted by sweety439

Reserve SR6 to n=100K, this is the sieve file.

Update the files. (only sieved to p=1e9)

[sweety439]

Originally Posted by sweety439

Update the files. (only sieved to p=1e9)

S6 currently at n=26312, 2 (probable) primes found:

(152249*6^25389+1)/5
(170199*6^25398+1)/5

R6 curremtly at n=27900, 1 (probable) prime found:

(2626*6^27871-1)/5

Continue reserving to n=100K...

[sweety439]

S6 currently at n=33325, 4 additional (probable) primes found:

(45634*6^26606+1)/5
(144509*6^28178+1)/5
(17464*6^29081+1)/5
(93589*6^31991+1)/5

R6 currently at n=40022, 2 additional (probable) primes found:

(2626*6^29061-1)/5
(2626*6^38681-1)/5

Continue reserving to n=100K...

[MisterBitcoin]

Originally Posted by sweety439

S6 currently at n=33325, 4 additional (probable) primes found:

(45634*6^26606+1)/5
(144509*6^28178+1)/5
(17464*6^29081+1)/5
(93589*6^31991+1)/5

R6 currently at n=40022, 2 additional (probable) primes found:

(2626*6^29061-1)/5
(2626*6^38681-1)/5

Continue reserving to n=100K...

Are you reporting your PRP´s to FactorDB?
You can also run primo to verify if its prime or composite.

[sweety439]

Found another (probable) prime:

(101529*6^33532+1)/5

[sweety439]

Originally Posted by MisterBitcoin

Are you reporting your PRP´s to FactorDB?
You can also run primo to verify if its prime or composite.

Yes, I have reported all of them to FactorDB, and all of them are probable primes.

You can reserve the extended Sierpinski/Riesel conjectures, see http://www.mersennewiki.org/index.ph..._definition%29 and http://www.mersennewiki.org/index.ph..._definition%29 for the current status.

[sweety439]

Originally Posted by MisterBitcoin

Are you reporting your PRP´s to FactorDB?
You can also run primo to verify if its prime or composite.

I use pfgw for them, and I use srsieve and sr2sieve to make the sieve file (they can only run even bases, since they cannot run the case such that both of k and b are odd).

[sweety439]

Originally Posted by sweety439

Yes, I have reported all of them to FactorDB, and all of them are probable primes.

You can reserve the extended Sierpinski/Riesel conjectures, see http://www.mersennewiki.org/index.ph..._definition%29 and http://www.mersennewiki.org/index.ph..._definition%29 for the current status.

Extended Sierpinski problem:

Finding and proving the smallest k such that (k*b^n+1)/gcd(k+1,b-1) is not prime for all integers n>=1.

Extended Riesel problem:

Finding and proving the smallest k such that (k*b^n-1)/gcd(k-1,b-1) is not prime for all integers n>=1.

[sweety439]

Originally Posted by sweety439

Extended Sierpinski problem:

Finding and proving the smallest k such that (k*b^n+1)/gcd(k+1,b-1) is not prime for all integers n>=1.

Extended Riesel problem:

Finding and proving the smallest k such that (k*b^n-1)/gcd(k-1,b-1) is not prime for all integers n>=1.

All n must be >= 1.

k-values that make a full covering set with all or partial algebraic factors are excluded from the conjectures.

k-values that are a multiple of base (b) and where (k+-1)/gcd(k+-1,b-1) (+ for Sierpinski, - for Riesel) is not prime are included in the conjectures but excluded from testing.
Such k-values will have the same prime as k / b.

[sweety439]

Originally Posted by sweety439

Yes, I have reported all of them to FactorDB, and all of them are probable primes.

You can reserve the extended Sierpinski/Riesel conjectures, see http://www.mersennewiki.org/index.ph..._definition%29 and http://www.mersennewiki.org/index.ph..._definition%29 for the current status.

These are the conjectured smallest extended Sierpinski/Riesel numbers for bases 2<=b<=1024, searched up to k=1M.