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May 12 at 0:39 comment added Sidharth Ghoshal Your "sneaking suspicion" was correct. See my answer. The solution to the divergent regularization sum of the reciprocals of the primes is Merten's constant: en.wikipedia.org/wiki/Meissel%E2%80%93Mertens_constant (surprisingly this is easier to derive than the divergent sum of the primes, which I don't think anyone has done yet (is prime zeta function even defined at -1?)).
Oct 29, 2009 at 4:34 history answered Harrison Brown CC BY-SA 2.5