has some pages with explanations involving the Jacobi function J, elliptic
curves and other mathematical esoterica.  Unfortunately it does not seem
likely that an explanation suitable for a college senior is available,
unless he is willing to educate himself for several months on higher

Hal Finney

> Exp(Pi*Sqrt(n)) Page
> This table lists values of Exp(Pi*Sqrt(n)), for some selected values of
> n up to 1000. Some of these values are very close to integers. A prize
> will be awarded to anyone who can either convincingly argue that this is
> coincidence, or who can explain why this is so in terms intelligible to
> an intelligent college senior. Something else that might help to lift
> the veil on this mystery would be a predictor: for a given value of n,
> is Exp(Pi*Sqrt(n)) close to an integer?
> ...
> 163                          262537412640768743.9999999999992
> ...

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