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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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Determination of the primality of $N$ by using factors of $N^{2}\pm 1$
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by H. C. Williams and J. S. Judd PDF
Math. Comp. 30 (1976), 157-172 Request permission

Abstract:

Algorithms are developed which can be used to determine the primality of a large integer N when a sufficient number of prime factors of ${N^2} + 1$ are known. A test for the primality of N which makes use of known factors of $N - 1,N + 1$ and ${N^2} + 1$ and the factor bounds on these numbers is also presented. In order to develop the necessary theory, the properties of some functions which are a generalization of Lehmer functions are used. Several examples of numbers proved prime by employing these tests are given.
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Additional Information
  • © Copyright 1976 American Mathematical Society
  • Journal: Math. Comp. 30 (1976), 157-172
  • MSC: Primary 10A25
  • DOI: https://doi.org/10.1090/S0025-5718-1976-0396390-3
  • MathSciNet review: 0396390