# sum of the reciprocal of the primes squared

Does anyone know of any information/work on this sum? I found absolutely nothing on the web about it.

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Naive question: why does one expect the value of this sum to have interesting properties? –  Yemon Choi Jan 27 '11 at 3:47
Ah, I see that someone more learned than me has provided links below, which presumably answer my question –  Yemon Choi Jan 27 '11 at 3:49

This would be $P(2)$, where $P$ is the "prime zeta function," q.v.
EDIT: A more recent source is Steven R Finch, Mathematical Constants, page 95: The sum of the squared reciprocals of primes is $$N=\sum_p{1\over p^2}=\sum_{k=1}^{\infty}{\mu(k)\over k}\log(\zeta(2k))=0.4522474200\dots$$