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A search for Wilson primes. (English) Zbl 1370.11003

Summary: 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.

MSC:

11A07 Congruences; primitive roots; residue systems
11Y16 Number-theoretic algorithms; complexity

Software:

NTL; gmp; PARI/GP
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Full Text: DOI arXiv

References:

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