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Re: Numerology about the Apery Constant Zeta(3)

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  • mikeoakes2
    ... Even better: (exp(Pi*sqrt(163))-744)^(1/3) = 640319.999999999999999999999999390... See Cohen, CCANT, p.383, which explains where astonishing results such
    Message 1 of 9 , Mar 16, 2011
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      --- 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
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