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Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



Primes at a glance

Authors: R. K. Guy, C. B. Lacampagne and J. L. Selfridge
Journal: Math. Comp. 48 (1987), 183-202
MSC: Primary 11A41
MathSciNet review: 866108
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Abstract: Let $ N = B - L$, $ B \geqslant \vert L\vert$, $ \gcd (B,L) = 1$, $ p\vert BL$ for all primes $ p \leqslant \sqrt N $. Then N is 0, 1 or a prime. Writing N in this form suggests a primality and a squarefreeness test. If we also require that when the prime $ q\vert BL$ and $ p < q$ then $ p\vert BL$, we say that $ B - L$ is a presentation of N. We list all presentations found for any N. We believe our list is complete.

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

  • [1] D. H. Lehmer, "On a problem of Störmer," Illinois J. Math., v. 8, 1964, pp. 59-79. MR 0158849 (28:2072)
  • [2] D. H. Lehmer, "On the converse of Fermat's Theorem," Amer. Math. Monthly, v. 43, 1936, pp. 347-354. MR 1523680
  • [3] John Brillhart, D. H. Lehmer, J. L. Selfridge, Bryant Tuckerman & S. S. Wagstaff, Jr., Factorizations of $ {b^n} \pm 1$, $ b = 2,3,5,6,7,10,11,12$ up to high powers, Contemp. Math., vol. 22, Amer. Math. Soc., Providence, R. I., 1983. MR 715603 (84k:10005)

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Article copyright: © Copyright 1987 American Mathematical Society

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