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: 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.
- Leonard M. Adleman, Carl Pomerance, and Robert S. Rumely, On distinguishing prime numbers from composite numbers, Ann. of Math. (2) 117 (1983), no. 1, 173β206. MR 683806, DOI https://doi.org/10.2307/2006975
- Alan Borning, Some results for $k\,!\pm 1$ and $2\cdot 3\cdot 5\cdots p\pm 1$, Math. Comp. 26 (1972), 567β570. MR 308018, DOI https://doi.org/10.1090/S0025-5718-1972-0308018-5
- John Brillhart, D. H. Lehmer, and J. L. Selfridge, New primality criteria and factorizations of $2^{m}\pm 1$, Math. Comp. 29 (1975), 620β647. MR 384673, DOI https://doi.org/10.1090/S0025-5718-1975-0384673-1
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- Mark Templer, On the primality of $k!+1$ and $2\ast 3$ $\ast 5\ast \cdots \ast \,p+1$, Math. Comp. 34 (1980), no. 149, 303β304. MR 551306, DOI https://doi.org/10.1090/S0025-5718-1980-0551306-2
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Article copyright:
© Copyright 1982
American Mathematical Society