Comments on "forty-one"

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  • 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.

On 2012-09-15 at 07:00:25, Andrew said:

n^2+n+41 is prime for n=0,1,2,...,40.

40^2 + 40 + 41 = 41^2 ?

On 2012-09-15 at 07:52:23, g said:

Whoops! Yes, it should have been n^2 - n + 41, with a minus instead of a plus. Or I should have said "for n = -40, -39, ..., 38, 39" which would have made the original statement true. (With the minus sign it becomes -39.. 40 instead.)

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