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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 pseudoprimes to $25\cdot 10^{9}$
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by Carl Pomerance, J. L. Selfridge and Samuel S. Wagstaff PDF
Math. Comp. 35 (1980), 1003-1026 Request permission


The odd composite $n \leqslant 25 \cdot {10^9}$ such that ${2^{n - 1}} \equiv 1\;\pmod n$ have been determined and their distribution tabulated. We investigate the properties of three special types of pseudoprimes: Euler pseudoprimes, strong pseudoprimes, and Carmichael numbers. The theoretical upper bound and the heuristic lower bound due to Erdös for the counting function of the Carmichael numbers are both sharpened. Several new quick tests for primality are proposed, including some which combine pseudoprimes with Lucas sequences.
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Additional Information
  • © Copyright 1980 American Mathematical Society
  • Journal: Math. Comp. 35 (1980), 1003-1026
  • MSC: Primary 10A40; Secondary 10-04, 10A25
  • DOI:
  • MathSciNet review: 572872