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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.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


New primality criteria and factorizations of $2^{m}\pm 1$
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by John Brillhart, D. H. Lehmer and J. L. Selfridge PDF
Math. Comp. 29 (1975), 620-647 Request permission

Erratum: Math. Comp. 39 (1982), 747-757.
Erratum: Math. Comp. 39 (1982), 747.


A collection of theorems is developed for testing a given integer N for primality. The first type of theorem considered is based on the converse of Fermat’s theorem and uses factors of $N - 1$. The second type is based on divisibility properties of Lucas sequences and uses factors of $N + 1$. The third type uses factors of both $N - 1$ and $N + 1$ and provides a more effective, yet more complicated, primality test. The search bound for factors of $N \pm 1$ and properties of the hyperbola $N = {x^2} - {y^2}$ are utilized in the theory for the first time. A collection of 133 new complete factorizations of ${2^m} \pm 1$ and associated numbers is included, along with two status lists: one for the complete factorizations of ${2^m} \pm 1$; the other for the original Mersenne numbers.
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Additional Information
  • © Copyright 1975 American Mathematical Society
  • Journal: Math. Comp. 29 (1975), 620-647
  • MSC: Primary 10A25
  • DOI:
  • MathSciNet review: 0384673