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

[Peter Luschny]

> Georgi Guninski:
> Hmmm, according to the internet the search for Wolstenholme primes
> is only up to 10^9.

- Hans Havermann:
- After your initial post, I naively tried to verify (in Mathematica)
- the primes to this limit. It took a two-year-old machine 4.2 hours to
- get to the second Wolstenholme prime (2124679). I realized then that I
- wasn't going to achieve that goal and that it was for a similar reason
- (the difficulty of fast-computing the binomial) that researchers with
- better means hadn't progressed beyond 10^9.

I doubt this as an efficient search would not go via binomials,
rather via Bernoulli numbers and irregular primes.

> Georgi Guninski:
> Is there efficient software or references for searching
> for Wolstenholme primes?

Most relevant is (and can be found on the web):

R. J. McIntosh, On the converse of Wolstenholme’s Theorem,
Acta Arith 71 (1995) 381–389.

Look for Theorem 2.

I think it is overdue to push the 10^9 limit from 2007.
Georgi: Go ahead and find the third WP! ;-)

Peter