Re: Numerology about the Apery Constant Zeta(3)
- --- In firstname.lastname@example.org, "WarrenS" <warren.wds@...> wrote:
> --for example (this is not due to me; perhaps it was first noticed by Ramanujan?)
> exp(Pi * sqrt(n))
> is within 10^(-12) of being an integer if n=163.
> This is beyond what any kind of fitting contrivance would be expected to produce.
> Also, no other n<25000 gets you even within a 100,000 times further away
> from being an integer.
(exp(Pi*sqrt(163))-744)^(1/3) = 640319.999999999999999999999999390...
See Cohen, CCANT, p.383, which explains where astonishing results such as these come from.