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Primes of the form $ n!\pm 1$ and $ 2\cdot 3\cdot 5\cdots p\pm 1$


Authors: J. P. Buhler, R. E. Crandall and M. A. Penk
Journal: Math. Comp. 38 (1982), 639-643
MSC: Primary 10A25; Secondary 10A10
DOI: https://doi.org/10.1090/S0025-5718-1982-0645679-1
Corrigendum: Math. Comp. 40 (1983), 727.
Corrigendum: Math. Comp. 40 (1983), 727.
MathSciNet review: 645679
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Abstract | References | Similar Articles | Additional Information

Abstract: All primes less than $ {10^{1000}}$ of the form $ n! \pm 1$ or $ 2 \cdot 3 \cdot 5 \cdots p \pm 1$ are determined. Results of Brillhart, Lehmer, and Selfridge are used together with a fast algorithm that applies to primality tests of integers N for which many factors of $ N \pm 1$ are known.


References [Enhancements On Off] (What's this?)

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  • [2] A. Borning, "Some results for $ k! + 1$ and $ 2 \cdot 3 \cdot 5 \cdots p + 1$," Math. Comp., v. 26, 1972, pp. 567-570. MR 0308018 (46:7133)
  • [3] J. Brillhart, D. H. Lehmer & J. L. Selfridge, "New primality criteria and factorizations of $ {2^m} \pm 1$," Math. Comp., v. 29, 1975, pp. 620-647. MR 0384673 (52:5546)
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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1982-0645679-1
Article copyright: © Copyright 1982 American Mathematical Society

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