> At 03:43 PM 3/11/99 -0300, Nicolau C. Saldanha wrote:
>
> >Some mathematician asked (conjectured?) whether M(M(M(M(...(2)...)))
> >is always prime; the first unknown case is M(M127),
>
> Another version of the conjecture is that M(M(p)) is prime where M(p) is a
> Mersenne prime. I think that the first one that fails to be prime is
> M(8191) = M(M(13)).
I.J. Good discusses this conjecture in his paper "Conjectures
Concerning Mersenne Numbers," MTAC(Math. Comp.), v.9, pp. 120-121, 1955.
He suggests the probability of M(M127) being prime is negligible.
Also see Robinson's paper in Luke's bibliography
http://www.scruznet.com/~luke/lit/lit_024s.htm
Will Edgington maintains a status of these numbers at
http://www.garlic.com/~wedgingt/MMPstats.txt
Links to programs that can factor these numbers can be found on
the Mersenne freeware page at
http://www2.netdoor.com/~acurry/mersenne/freeware.html
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