A search for Wilson primes

Costa, Edgar; Gerbicz, Robert; Harvey, David

doi:10.1090/S0025-5718-2014-02800-7

A search for Wilson primes
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by Edgar Costa, Robert Gerbicz and David Harvey;

Math. Comp. 83 (2014), 3071-3091

DOI: https://doi.org/10.1090/S0025-5718-2014-02800-7

Published electronically: January 27, 2014

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Abstract:

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

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