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A search for Wilson primes


Authors: Edgar Costa, Robert Gerbicz and David Harvey
Journal: Math. Comp. 83 (2014), 3071-3091
MSC (2010): Primary 11A07; Secondary 11Y16
DOI: https://doi.org/10.1090/S0025-5718-2014-02800-7
Published electronically: January 27, 2014
MathSciNet review: 3246824
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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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Additional Information

Edgar Costa
Affiliation: Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, New York 10012-1185
Email: edgarcosta@nyu.edu

Robert Gerbicz
Affiliation: Eötvös Loránd University, H-1117 Budapest, Pázmány Péter sétány 1/C, Hungary
Email: robert.gerbicz@gmail.com

David Harvey
Affiliation: School of Mathematics and Statistics, University of New South Wales, Sydney NSW 2052, Australia
Email: d.harvey@unsw.edu.au

DOI: https://doi.org/10.1090/S0025-5718-2014-02800-7
Received by editor(s): October 31, 2012
Received by editor(s) in revised form: December 5, 2012, January 31, 2013, and February 3, 2013
Published electronically: January 27, 2014
Additional Notes: The first author was partially supported by FCT doctoral grant SFRH/BD/ 69914/2010.
The third author was partially supported by the Australian Research Council, DECRA Grant DE120101293.
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.