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 2023-02-11, 08:36 #133 kar_bon     Mar 2006 Germany 22·13·59 Posts 4*5^n+1 I've just changed the type of that reservation: The template for Williams primes were implemented before the capability of storing Proth primes in any base. So I've cretead the (more general) Proth prime for this Williams prime, which obtains the data from that new page. Each page links to the other for easy navigation. This should be done with all somtimes in the future.
 2023-02-11, 18:48 #134 Citrix     Jun 2003 7·233 Posts Proth primes are limited to base 2 by definition. https://en.wikipedia.org/wiki/Proth_prime
2023-02-11, 19:28   #135
Happy5214

"Alexander"
Nov 2008
The Alamo City

102810 Posts

Quote:
 Originally Posted by Citrix Proth primes are limited to base 2 by definition. https://en.wikipedia.org/wiki/Proth_prime
Allegedly, numbers of the form k*b^n+1, b ≠ 2, are called generalized Proth numbers, though https://arxiv.org/pdf/2207.12407.pdf is the only explicit source I could find for that outside of a few forum posts from over a decade ago.

 2023-02-12, 12:19 #136 kar_bon     Mar 2006 Germany 22·13·59 Posts As stated in the definition of Proth primes in PrimeWiki I also allow all primes listed with k<2^n. The other reason for naming that way is to handle the template and categorization easier to store any number of the form k*b^n+1, the same for Riesel side.
 2023-02-14, 06:58 #137 kar_bon     Mar 2006 Germany BFC16 Posts Because Ryan Propper is again poaching (submitted 3 new primes found to Top5000) a reserved range, Citrix has canceld his for 4*5^n+1. @Propper: Stop stealing others work, the community will recognize this and is not amused!

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