Primes at a glance
HTML articles powered by AMS MathViewer
- by R. K. Guy, C. B. Lacampagne and J. L. Selfridge PDF
- Math. Comp. 48 (1987), 183-202 Request permission
Abstract:
Let $N = B - L$, $B \geqslant |L|$, $\gcd (B,L) = 1$, $p|BL$ 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 $q|BL$ and $p < q$ then $p|BL$, 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
- D. H. Lehmer, On a problem of Störmer, Illinois J. Math. 8 (1964), 57–79. MR 158849
- D. H. Lehmer, On the Converse of Fermat’s Theorem, Amer. Math. Monthly 43 (1936), no. 6, 347–354. MR 1523680, DOI 10.2307/2301798
- John Brillhart, D. H. Lehmer, J. L. Selfridge, Bryant Tuckerman, and S. S. Wagstaff Jr., Factorizations of $b^{n}\pm 1$, Contemporary Mathematics, vol. 22, American Mathematical Society, Providence, R.I., 1983. $b=2,\,3,\,5,\,6,\,7,\,10,\,11,\,12$ up to high powers. MR 715603
Additional Information
- © Copyright 1987 American Mathematical Society
- Journal: Math. Comp. 48 (1987), 183-202
- MSC: Primary 11A41
- DOI: https://doi.org/10.1090/S0025-5718-1987-0866108-3
- MathSciNet review: 866108