On Tue, 16 Mar 1999, Brian J Beesley wrote:
> Suggest you look at the following references, which I just found by
> following links from Chris Caldwell's Web site.
>
> J. W. Bruce, "A really trivial proof of the Lucas-Lehmer test," Amer.
> Math. Monthly, April (1993) 370-371. (Proves sufficiency only. See
> also M. I. Rosen "A proof of the Lucas-Lehmer test," Amer.
> Math. Monthly, 95 (1988) 855-856.)
> >
Perhaps the ideal reference, if you are serious, is the new text "E'douard
Lucas and Primality Testing" by Hugh C. Williams (Canadian Math. Soc.
Series of Monographs and Advanced Texts, v22, Wiley-Interscience, 1998).
This is an excellent history of primality proving--every math library
ought to buy a copy.
> > To prove that M(127) (Or M127, whichever refers to 2^127 - 1, not the 127th
> > Mersenne prime) is prime, did Lucas use his test by hand? I know he did it by
> > hand, at the very least.
>
> Very probably. Lucas was working in the time before efficient
> calculating machines were in common usage (at any rate, in the
> West; the Russians, Chinese and Japanese were using their
He used a 127 by 127 chessboard (see the above text, section 3.2: Lucas
and M127).
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