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Lucasian Criteria for the Primality of N = h · 2n - 1

Hans Riesel
Mathematics of Computation
Vol. 23, No. 108 (Oct., 1969), pp. 869-875
DOI: 10.2307/2004975
Stable URL: http://www.jstor.org/stable/2004975
Page Count: 7
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Abstract

Let vi = v2i-1 - 2 with v0 given. If $v_{n - 2} \equiv 0 (\operatorname{mod} N)$ is a necessary and sufficient criterion that N = h · 2n - 1 be prime, this is called a Lucasian criterion for the primality of N. Many such criteria are known, but the case h = 3A has not been treated in full generality earlier. A theorem is proved that (by aid of computer) enables the effective determination of suitable numbers v0 for any given N, if $h < 2^n$. The method is used on all N in the domain h = 3(6)105, n ≤ 1000. The Lucasian criteria thus constructed are applied, and all primes N = h · 2n - 1 in the domain are tabulated.

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