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Wednesday 2011-08-24

forty-one

  • n2+n+41 is prime for n=0,1,2,...,40.
  • 4×41−1 = 163, a Heegner number.
  • exp(π√163) = 262537412640768743.999999999999250... = 123(2312−1)3 + 744 − ε with ε very small.

These facts are not unrelated, but the connection between them is rather too esoteric to go into here. Besides, I don’t really understand it well.

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