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Could, or should, the ancient Greeks have discovered the Lucas-Lehmer test?

Granger, Robert (2015) Could, or should, the ancient Greeks have discovered the Lucas-Lehmer test? The Mathematical Gazette, 97 (539). pp. 242-255.

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Abstract

The Lucas-Lehmer (LL) test is the most efficient known for testing the primality of Mersenne numbers, i.e. the integers Ml = 2l − 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 l = 2,3,5,7, 13, 17, 19,31,67, 127 and 257. 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.

Item Type: Article
Divisions : Faculty of Engineering and Physical Sciences > Computing Science
Authors :
NameEmailORCID
Granger, Robertr.granger@surrey.ac.uk
Date : 23 January 2015
DOI : 10.1017/S0025557200005830
Depositing User : Clive Harris
Date Deposited : 06 Feb 2019 16:20
Last Modified : 06 Feb 2019 16:20
URI: http://epubs.surrey.ac.uk/id/eprint/850391

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