To Cruelty:

You are tested for (b-1)*b^n-1, which is the Riesel problem for the special case, k=b-1. According to the website

http://harvey563.tripod.com/wills.txt, there are some large primes found: (up to base b=500, exponent > 1000)

(38-1)*38^136211-1 (this website wrongly writes the exponent as 136221)

(83-1)*83^21495-1

(98-1)*98^4983-1

(113-1)*113^286643-1

(125-1)*125^8739-1

(188-1)*188^13507-1

(228-1)*228^3695-1

(347-1)*347^4461-1

(357-1)*357^1319-1

(401-1)*401^103669-1

(417-1)*417^21002-1

(443-1)*443^1691-1

(458-1)*458^46899-1

(494-1)*494^21579-1

etc.

The first few bases without known prime are 128, 233, 268, 293, 383, 478, 488, ..., I known that you only test base 128 because it is the first such base, but how about larger bases?

How about (b-1)*b^n+1, the Sierpinski problem for the same case, k=b-1? Recently, I searched this form for bases b up to 500, but found no prime for b = 122, 123, 180, 202, 249, 251, 257, 269, 272, 297, 298, 326, 328, 342, 347, 362, 363, 419, 422, 438, 452, 455, 479, 487, 497, 498. Some terms are given by the CRUS project:

http://www.noprimeleftbehind.net/cru...onjectures.htm.

Besides, how about (b+1)*b^n-1 and (b+1)*b^n+1 (the Sierpinski/Riesel problem for k=b+1)? You only tests the case b=3. (Of course, for the case (b+1)*b^n+1, b should not = 1 (mod 3), or all the numbers of this form are divisible by 3 and cannot be prime)