--- In

primenumbers@yahoogroups.com, "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.

Even better:

(exp(Pi*sqrt(163))-744)^(1/3) = 640319.999999999999999999999999390...

See Cohen, CCANT, p.383, which explains where astonishing results such as these come from.

Mike