Hiya Henrik,
I did mean for 2^p-1; p prime.
That's why I work in Computing not the discipline of Maths :-)
I am certain that the graph in Knuth sect 4.5.4 (which by luck
I had only read for the first time last night) is definately
not applicable to Mersenne numbers (with prime exponent).
I am certain that there is a minimum size for any divisor of a
Mersenne (conversely there is a maximum order of 2 mod f for a
candidate factor f) such that there is therefore a maximum size
for the largest factor.
This makes the cumulative frequency graph hit 1.0 before 100%!
(I had best be precise so that one day I grow up to be a good
Mathematician, - ignoring the factorisation 1 & itself).
Can we do some statistics on the (complete) factorisations
we already have?
I am also sure that in many other ways Mersennes do not behave
like random numbers as discussed in sect 4.5.4.
I think I am correct in what I meant to say, that it hasn't
been proved that there are an infinite number of Mersenne
Primes or an infinite number of Mersenne's with prime exponent
that are composite or both with a limiting ratio.
Thanks Henrik for encouraging me to be precise in the presense
of real Mathematicians.
Cheers,
Paul Landon
Henrik Olsen wrote:
> On Mon, 24 Jan 2000, Paul Landon wrote:
> > Subject: Re: Mersenne: Size of largest prime factor
> >[snip]
> > This is not new news to most people here, but I have to remind
> > myself, it still hasn't been proved whether there are an infinite
> > number of Mersenne Primes or an infinite number of Mersenne
> > composites.
> Erhm?
> 2^n-1 where n is composite is in itself composite, so showing that there
> are infinitely many Mersenne composites is easy. :)
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