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 2016-07-01, 00:05 #45 Cruelty     May 2005 2·809 Posts status report k=2 and k=4 @ base=3 tested till n=1.54M 127*128^n-1 tested till n=1.37M
 2016-08-31, 22:37 #46 Cruelty     May 2005 2·809 Posts status report k=2 and k=4 @ base=3 tested till n=1.55M 127*128^n-1 tested till n=1.42M
 2016-10-01, 13:34 #47 Cruelty     May 2005 110010100102 Posts k=2 and k=4 @ base=3 tested till n=1.55M - doublechecking several ranges 127*128^n-1 tested till n=1.46M
 2016-11-01, 23:53 #48 Cruelty     May 2005 2·809 Posts status report k=2 and k=4 @ base=3 tested till n=1.55M - doublechecking several ranges 127*128^n-1 tested till n=1.5M
 2016-11-30, 22:16 #49 Cruelty     May 2005 2×809 Posts status report k=2 and k=4 @ base=3 tested till n=1.55M - doublechecking several ranges 127*128^n-1 tested till n=1.51M
2016-12-03, 16:16   #50
sweety439

Nov 2016

9C216 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, 122 views)

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

 2016-12-05, 10:44 #51 Cruelty     May 2005 2×809 Posts Indeed I am searching for those so called Williams Primes, already found some at base = 3 and one at base = 113. Currently I am focusing on base 128 and 3. I will consider next base after finding prime for b=128, so you're free to reserve any other base Just let know Steven Harvey about it. I don't know whether someone is searching for similar primes on the "+" side however.
 2016-12-05, 14:17 #52 sweety439     Nov 2016 2·1,249 Posts Why you don't search (b-1)*b^n+1? In http://oeis.org/A087139, someone is searching it for prime b, just as in http://oeis.org/A122396, someone is searching (b-1)*b^n-1 for prime b. According to http://oeis.org/A087139, the b=251 case for (b-1)*b^n+1 is searched to n=73000, no prime was found. However, there is also no known prime for bases b=122, 123, 180, 202, ..., why you don't search (b-1)*b^n+1 for b=122? I searched (b-1)*b^n+1 for all bases 2<=b<=500, but only tested n<=1024. (except of the primes (88-1)*88^3022+1 and (158-1)*158^1620+1) Besides, you said "k=2 and k=4 @ base=3 tested ...", are you searching all of the four families? (3-1)*3^n-1, (3-1)*3^n+1, (3+1)*3^n-1, and (3+1)*3^n+1? Last fiddled with by sweety439 on 2016-12-05 at 14:28
 2017-01-01, 01:26 #53 Cruelty     May 2005 2×809 Posts status report k=2 and k=4 @ base=3 tested till n=1.56M 127*128^n-1 tested till n=1.53M Concerning my b=3 effort, I am posting this status in Riesel Prime Search, so I mean that I am working only on 2*3^n-1 and 4*3^n-1
 2017-01-31, 22:39 #54 Cruelty     May 2005 2·809 Posts status report k=2 and k=4 @ base=3 tested till n=1.57M 127*128^n-1 tested till n=1.57M
 2017-04-01, 00:43 #55 Cruelty     May 2005 2·809 Posts status report k=2 and k=4 @ base=3 tested till n=1.6M 127*128^n-1 tested till n=1.59M