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2016-12-03, 16:16   #50
sweety439

"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36

5·7·83 Posts

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)
Attached Files
 least k such that (n-1)n^k+1 is prime.txt (3.6 KB, 191 views)

Last fiddled with by sweety439 on 2016-12-03 at 16:23