A Sierpinski/Riesel-like problem

[sweety439]

SR112 were also done, tested to n=1000.

Note:

In R112:

All k where k = m^2
and m = = 15 or 98 mod 113:
for even n let k = m^2
and let n = 2*q; factors to:
(m*112^q - 1) *
(m*112^q + 1)
odd n:
factor of 113

Thus, R112 k=225 proven composite by partial algebraic factors.

[sweety439]

For extended Sierpinski problem base b, the formula is (k*b^n+1)/gcd(k+1,b-1).

For extended Riesel problem base b, the formula is (k*b^n-1)/gcd(k-1,b-1).

Note:

k and b are integers, k>=1, b>=2.

All n must be integer.

All n must be >= 1.

"gcd" means "greatest common divisor".

gcd(0,m) = m for all integer m.

gcd(1,m) = 1 for all integer m.

[sweety439]

k-values 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]

S106 and R127 were also done, tested to n=1000.

Now, all Sierpinski and Riesel bases b<=128 with CK<=5000 are done!!!

[sweety439]

This is the text files for all Sierpinski and Riesel bases b<=64.

[sweety439]

This file include all Sierpinski and Riesel bases b<=128 (except R3, R6, SR40, SR52, SR66, S70, SR78, SR82, SR96, R106, SR120, SR124, SR126, S127) and Sierpinski and Riesel bases b = 256, 512 and 1024.

For SR2, SR15 and R36, only include the k's <= 10000.

For S6, SR24, SR28, R30, SR42, SR48, SR60, SR72, SR80, SR102, SR108, only include the k's not in CRUS, i.e. the k's such that gcd(k+-1,b-1) (+ for Sierpinski, - for Riesel) is not 1.

[sweety439]

These are text files for the CK for all bases <= 128 and all power of 2 bases <= 1024.

Note: I only tested the primes <= 30000, if a k has a covering set with at least one prime > 30000, then this k would be return non-Sierpinski (or non-Riesel) number.

[sweety439]

Reserve S113, S123, R107, R115 (only for k=4), R121, R123.

[sweety439]

Originally Posted by sweety439

Reserve S113, S123, R107, R115 (only for k=4), R121, R123.

Found these (probable) primes:

(13*113^1336+1)/14

Thus S113 is now 1k base.

[sweety439]

Update the newest text file for some Sierpinski bases.

[sweety439]

Update the newest text file for some Riesel bases.