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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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The continuing search for Wieferich primes
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by Joshua Knauer and Jörg Richstein PDF
Math. Comp. 74 (2005), 1559-1563 Request permission

Abstract:

A prime $p$ satisfying the congruence \[ 2^{p-1} \equiv 1 \pmod {p^2}\] is called a Wieferich prime. Although the number of Wieferich primes is believed to be infinite, the only ones that have been discovered so far are $1093$ and $3511$. This paper describes a search for further solutions. The search was conducted via a large scale Internet based computation. The result that there are no new Wieferich primes less than $1.25 \cdot 10^{15}$ is reported.
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Additional Information
  • Joshua Knauer
  • Affiliation: Department of Mathematics, Simon Fraser University, Burnaby, British Columbia, V5A 1S6 Canada
  • Email: jknauer@cecm.sfu.ca
  • Jörg Richstein
  • Affiliation: Institut für Informatik, Justus-Liebig-Universität, Gießen, Germany
  • Email: Joerg.Richstein@informatik.uni-giessen.de
  • Received by editor(s): June 18, 2003
  • Received by editor(s) in revised form: April 11, 2004
  • Published electronically: January 19, 2005
  • Additional Notes: The second author was supported in part by the Killam Trusts.
  • © Copyright 2005 American Mathematical Society
  • Journal: Math. Comp. 74 (2005), 1559-1563
  • MSC (2000): Primary 11A07; Secondary 11-04
  • DOI: https://doi.org/10.1090/S0025-5718-05-01723-0
  • MathSciNet review: 2137018