Abstract
We suggest an algorithm to test numbers of the form N = 2kpm − 1 for primality, where 2k < pm, k is an odd positive integer, 2k < pm, p is a prime number, and p = 3 (mod 4). The algorithm makes use of the Lucas functions. First we present an algorithm to test numbers of the form N = 2k3m − 1. Then the same technique is used in the more general case where N = 2kpm − 1. The algorithms suggested here are of complexity O((log N)2 log log N log log log N).
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