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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.78.

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Strong pseudoprimes to twelve prime bases
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by Jonathan Sorenson and Jonathan Webster PDF
Math. Comp. 86 (2017), 985-1003 Request permission


Let $\psi _m$ be the smallest strong pseudoprime to the first $m$ prime bases. This value is known for $1 \leq m \leq 11$. We extend this by finding $\psi _{12}$ and $\psi _{13}$. We also present an algorithm to find all integers $n\le B$ that are strong pseudoprimes to the first $m$ prime bases; with reasonable heuristic assumptions we can show that it takes at most $B^{2/3+o(1)}$ time.
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Additional Information
  • Jonathan Sorenson
  • Affiliation: Department of Computer Science and Software Engineering, Butler University, Indianapolis, Indiana 46208
  • MR Author ID: 334195
  • Email:
  • Jonathan Webster
  • Affiliation: Department of Mathematics and Actuarial Science, Butler University, Indianapolis, Indiana 46208
  • MR Author ID: 903429
  • Email:
  • Received by editor(s): September 2, 2015
  • Published electronically: June 2, 2016
  • Additional Notes: This work was supported in part by a grant from the Holcomb Awards Committee.
  • © Copyright 2016 American Mathematical Society
  • Journal: Math. Comp. 86 (2017), 985-1003
  • MSC (2010): Primary 11Y11, 11Y16; Secondary 11A41, 68W40, 68W10
  • DOI:
  • MathSciNet review: 3584557