# [seqfan] Re: Software for searching for Wolstenholme primes?

Georgi Guninski guninski at guninski.com
Mon Nov 19 09:20:55 CET 2012

```Hmmm, according to the internet the search for Wolstenholme primes is
only up to 10^9.

IIRC searches for other rare primes are much higher ranges, maybe 10^14.

On Sun, Nov 18, 2012 at 06:30:29PM +0100, allouche at math.jussieu.fr wrote:
> Hmmm this is a question of residues modulo a power of p, not mod p.
> Wilson's theorem is mod p, and anyway a binomial coefficient can
> be easily computed mod p (using the base p expansion of its arguments
> this is a theorem of Legendre).
>
> It happens that binomial coefficients can be computed "sort of easily"
> modulo a prime power, see, e.g.,
> http://www.cecm.sfu.ca/organics/papers/granville/paper/binomial/html/node4.html#SECTION00040000000000000000
>
> Not sure this helps for Wolstenholme primes
>
> jean-paul
>
>
> David Wilson <davidwwilson at comcast.net> a écrit :
>
> >My guess would be probably not.
> >
> >If there were an efficient way to evaluate binomial coefficient
> >residues, then would be an efficient way to evaluate factorial (I
> >think), and we would all be using Wilson's theorem an efficient
> >deterministic primality test.
> >
> >On 11/17/2012 5:02 AM, Georgi Guninski wrote:
> >>Out of blind opportunism I am looking for efficient software for
> >>verifying if a prime is a  Wolstenholme prime A088164.
> >>
> >>The basic definition requires computing a binomial coefficient
> >>mod p^4.
> >>
> >>For this task found Max Alekseyev's pari binomod.gp, but it appears
> >>slow to me: for p=2124679 binomod took 6 seconds.
> >>
> >>Is there efficient software or references for searching
> >>for Wolstenholme primes?
> >>
> >>_______________________________________________
> >>
> >>Seqfan Mailing list - http://list.seqfan.eu/
> >>
> >
> >
> >_______________________________________________
> >
> >Seqfan Mailing list - http://list.seqfan.eu/
>
>
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/

```