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 p2. We report on a search for Wilson primes up to 2 × 1013, and describe several new algorithms that were used in the search. In particular we give the first known algorithm that computes (p–1)! mod p2 in average polynomial time per prime.

Data

The file 2e13.txt.bz2 (247MB) contains a list of all Wilson quotients wp such that p < 2 × 1013 and |wp/p| < 1/50000. Each line contains the prime p followed by the quotient wp.


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