Could , or should the ancient Greeks have discovered the Lucas - Lehmer test ? ROBERT GRANGER
نویسنده
چکیده
The Lucas-Lehmer (LL) test is the most efficient known for deterministically testing the primality of Mersenne numbers, i.e., the integers Ml = 2 l − 1, for l ≥ 1. The Mersenne numbers are so-called in honour of the French scholar Marin Mersenne (1588-1648), who in 1644 published a list of exponents l ≤ 257 which he conjectured produced all and only those Ml which are prime, for l in this range, namely 1 l = 2, 3, 5, 7, 13, 17, 19, 31, 67, 127 and 257 [1]. Mersenne’s list turned out to be incorrect, omitting the prime-producing l = 61, 89 and 107 and including the composite-producing l = 67 and 257, although this was not finally confirmed until 1947, using both the LL test and contemporary mechanical calculators [2]. The LL test is based on the following theorem.
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