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Mathematics of Computation

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Effective primality tests for some integers of the forms $ A5\sp n-1$ and $ A7\sp n-1$

Author: H. C. Williams
Journal: Math. Comp. 48 (1987), 385-403
MSC: Primary 11Y11; Secondary 11A51
MathSciNet review: 866123
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Abstract: It is shown how polynomial time prime tests, which are both fast and deterministic, can be developed for many numbers of the form $ A{r^n} - 1\;(r = 5,7;A < {r^n})$. These tests, like the Lucas-Lehmer test for the primality of the Mersenne numbers, are derived by using the properties of the Lucas functions. We exemplify these ideas by using numbers of the form $ 2 \cdot {10^n} - 1$.

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Article copyright: © Copyright 1987 American Mathematical Society