A Sierpinski/Riesel-like problem

[sweety439]

Originally Posted by sweety439

Reserving SR456

R946 has larger CK, compare with S946, which has CK = 3963194 and covering set {3, 13, 73, 373, 947}, period = 12

Bases with CK > 5M are:

66 (both sides, Sierpinski CK is known to be 21314443 and Riesel CK is known to be 63717671)

120 (both sides, Sierpinski CK is unknown and Riesel CK is known to be 166616308)

156 (both sides, CK for both sides are both unknown)

180 (Riesel side, CK = 7674582, the CK for Sierpinski side is only 1679679)

210 (both sides, Sierpinski CK is known to be 147840103 and Riesel CK is known to be 50718493)

280 (both sides, CK for both sides are both unknown)

330 (both sides, Sierpinski CK is known to be 11091478 and Riesel CK is known to be 11200379)

358 (both sides, Sierpinski CK is known to be 9330411 and Riesel CK is known to be 9202246)

420 (Riesel side, CK = 6548233, the CK for Sierpinski side is only 2288555)

456 (both sides, CK for both sides are now reserving ....)

462 (Sierpinski side, CK = 6880642, the CK for Riesel side is only 2924772)

546 (reserved)

570 (Riesel side, CK = 12511182, the CK for Sierpinski side is only 2972056)

630 (reserved)

690 (reserved)

726 (reserved)

728 (the original CK for both sides are both wrong, since the covering sets for the true CK for both sides have a large prime (105997), thus I didn't find them, the CK for the Sierpinski side is 953974 and the CK for the Riesel side is 212722)

756 (reserved)

876 (reserved)

910 (both sides, CK for both sides are both unknown)

946 (Riesel side, CK is now reserving, the CK for Sierpinski side is only 3963194)

960 (both sides, CK for both sides are both unknown)

966 (reserved)

1008 (Sierpinski side, CK is now reserving, the CK for Riesel side is only 623563)

1020 (reserved)

* Note: I will not reserve bases 156, 280, 910, and 960, since the upper bound of the CK for these bases (for both sides) are too large.

Reserve the CK for S1008, since it is the only CK (beside current-reserving S120 and R946) such that only one side has known CK

Also reserve the CK for R1216, since the first bases b>1024 with unknown Sierpinski CK are 1170, 1236, 1320, but the first bases b>1024 with unknown Riesel CK are 1170, 1216, 1236, 1320

[sweety439]

The CK for S1008 is now known to be 12730554

[sweety439]

The CK for R1216 is now known to be 13675428

[sweety439]

The CK for S120 is now known to be 374876369

[sweety439]

Update files to include the known CK's and covering sets for SR66 and SR120

Sierpinski

Riesel

[sweety439]

The CK for S630 is now known to be 24015859
The CK for R630 is now known to be 24412760

[sweety439]

Note: I only searched the primes <= 50000, and only searched (k*b^n+-1)/gcd(k+-1,b-1) for 1<=n<=3000

[sweety439]

Now, all CK for both sides for bases 2<=b<=689 (except 156 and 280) are known.

[sweety439]

Originally Posted by sweety439

The CK for R1216 is now known to be 13675428

For the conjecture of R1216, all k = m^2 with m == 78 or 1139 mod 1217 and all k = 19*m^2 with m == 593 or 624 mod 1217 proven composite by partial algebra factors.

[sweety439]

Originally Posted by sweety439

Found two CK's:

S456 has CK = 14836963
R456 has CK = 14629026

For the conjecture of R456, all k = m^2 with m == 109 or 348 mod 457 and all k = 114*m^2 with m == 218 or 239 mod 457 proven composite by partial algebra factors.

[sweety439]

Sierpinski problem base b (b>=2): 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

Riesel problem base b (b>=2): 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