*n*^{2}+*n*+41 is prime for*n*=0,1,2,...,40.- 4×41−1 = 163, a Heegner number.
- exp(π√163) = 262537412640768743.999999999999250... = 12
^{3}(231^{2}−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 07:52:23,
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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40^2 + 40 + 41 = 41^2 ?