A search for Wilson primes

2012/09/15 by Costa, Edgar, Gerbicz, Robert, Harvey, David · 2 citations
#11A07 (Primary) 11Y16 (Secondary) #Data Structures and Algorithms (cs.DS) #FOS: Computer and information sciences #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1209.3436

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.

Cited by

• Wilson's theorem modulo higher prime powers II: Bernoulli numbers and polynomials
• Quantum Algorithms for Modular Factorials

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