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

allouche at math.jussieu.fr allouche at math.jussieu.fr
Sun Nov 18 18:30:29 CET 2012

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.,

Not sure this helps for Wolstenholme primes


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?
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