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There is a prime generating formula n^2 + n + 41 for n=0 to 39. Maybe this is related?

Yes it is, it is a bit hidden on the left side on the page in a details box.

This also holds for n = -1. Not much real benefit; just extends the set of n to 41 consecutive integers.

The P+41 spiral contains an unusually large number of primes because 163 is a Heegner number (https://en.wikipedia.org/wiki/Heegner_number).

It's difficult to visually diff these on mobile, but P+41 appears to mirror S-9.