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Mathematics of Computation

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Some observations on primality testing

Authors: H. C. Williams and R. Holte
Journal: Math. Comp. 32 (1978), 905-917
MSC: Primary 10A25; Secondary 10-04
MathSciNet review: 0476625
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Abstract: Let N be an integer which is to be tested for primality. Previous methods of ascertaining the primality of N make use of factors of $ N \pm 1$, $ {N^2} \pm N + 1$, and $ {N^2} + 1$ in order to increase the size of any possible prime divisor of N until it is impossible for N to be the product of two or more primes. These methods usually 2 work as long as $ N < {K^2}$ , where K is $ 1/12$ of the product of the known prime power factors of $ N \pm 1$, $ {N^2} \pm N + 1$, and $ {N^2} + 1$. In this paper a technique is described which, when used in conjunction with these methods, will often determine the pri mality of N when $ N < l{K^3}$ and l is small.

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Article copyright: © Copyright 1978 American Mathematical Society

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