Comments on "forty-one"

[Hide] original entry

• 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.