- **Riesel Prime Search**
(*https://www.mersenneforum.org/forumdisplay.php?f=59*)

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(*https://www.mersenneforum.org/showthread.php?t=8765*)

status reportk=2 and k=4 @ base=3 tested till n=1.54M
127*128^n-1 tested till n=1.37M |

status reportk=2 and k=4 @ base=3 tested till n=1.55M
127*128^n-1 tested till n=1.42M |

k=2 and k=4 @ base=3 tested till n=1.55M - doublechecking several ranges
127*128^n-1 tested till n=1.46M |

status reportk=2 and k=4 @ base=3 tested till n=1.55M - doublechecking several ranges
127*128^n-1 tested till n=1.5M |

status reportk=2 and k=4 @ base=3 tested till n=1.55M - doublechecking several ranges
127*128^n-1 tested till n=1.51M |

1 Attachment(s)
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 [URL]http://harvey563.tripod.com/wills.txt[/URL], 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: [URL]http://www.noprimeleftbehind.net/crus/Sierp-conjectures.htm[/URL]. 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) |

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 :smile: Just let know Steven Harvey about it.
I don't know whether someone is searching for similar primes on the "+" side however. |

Why you don't search (b-1)*b^n+1? In [URL]http://oeis.org/A087139[/URL], someone is searching it for prime b, just as in [URL]http://oeis.org/A122396[/URL], someone is searching (b-1)*b^n-1 for prime b.
According to [URL]http://oeis.org/A087139[/URL], 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? |

status reportk=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 :smile: |

status reportk=2 and k=4 @ base=3 tested till n=1.57M
127*128^n-1 tested till n=1.57M |

status reportk=2 and k=4 @ base=3 tested till n=1.6M
127*128^n-1 tested till n=1.59M |

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