# A search for Wilson primes

(with Edgar Costa and Robert Gerbicz)

Math. Comp. **83** (2014), 3071–3091 (DOI).

arXiv preprint (September 2012).

## Abstract

A Wilson prime is a prime *p* such that (*p*–1)! = –1 mod *p*^{2}. We report on a search for Wilson primes up to 2 × 10^{13}, and describe several new algorithms that were used in the search. In particular we give the first known algorithm that computes (*p*–1)! mod *p*^{2} in average polynomial time per prime.

## Data

The file 2e13.txt.bz2 (247MB) contains a list of all Wilson quotients *w*_{p} such that *p* < 2 × 10^{13} and |*w*_{p}/*p*| < 1/50000. Each line contains the prime *p* followed by the quotient *w*_{p}.

Back to the main page