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

[allouche at math.jussieu.fr]

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?
>>
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