Alan Simpson wrote:
> hi everyone,
>
> there have been several messages lately about this conjecture that the n-th
> Mersenne prime is "around" (3/2)^{n}.
>
>
> (1)
> However, no one seems to have mentioned Wagstaff's paper in Math. Comp.
> (1982 or 1983).
> ...
> (2)
> . But do people have any
> mathematical arguments (a la heuristic of Wagstaff) for supporting this 3/2
> value? And a pile of other related questions that I can't articulate this
> early in the morning.
>
> Alan Simpson
>
>
> Ad 1) Really, I did not read Wagstaff's paper. I shall try to retrieve.
> Ad 2) Denoting by
> S(n) =the sum of divisors of the natural number "n",
> P(n)= the partition function of the natural number "n"
> and E(n) = the Euler-coefficients of the famous Euler formula
>
> it is known that n
> ------
> S(n)= \ E(i)*P(n-i)
> /
> ------
> i=1
> (the so-called Cauchy multiplication)
> So the S(n) function , - and therefore the Mersenne problem, too - is somehow
> in relation with the partition function. The quoted
> Hardy-Ramanujan-Rademacher formula contains the "PI*SQRT(2)/3"
> expression.
> I know, other factors should be found, and I hope, someone would.
Regards
Paul La'ng
Budapest, Hungary
>
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