# Sum of the reciprocals of the primes squared

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

• Naive question: why does one expect the value of this sum to have interesting properties? Jan 27, 2011 at 3:47
• Ah, I see that someone more learned than me has provided links below, which presumably answer my question Jan 27, 2011 at 3:49
• Kudos for not deleting "why does one expect the value of this sum to have interesting properties?" In retrospect, it was extremely degrading to Ethan Brush, wasn't it? - Well, he never came back to this site. Mar 8, 2021 at 18:16
• @niloderoock Your definition of "extremely degrading" doesn't agree with mine. Jan 20 at 20:17
• Something must have been deleted because I don't understand my own reaction from what I can see here. Jan 28 at 11:12

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 $$N=\sum_p{1\over p^2}=\sum_{k=1}^{\infty}{\mu(k)\over k}\log(\zeta(2k))=0.4522474200\dots$$