The sum of the reciprocals of ALL primes diverges to infinity. Read about it here:
https://en.wikipedia.org/wiki/Divergence_of_the_sum_of_the_reciprocals_of_the_primes
However, the sum of the reciprocals of the SQUARES of ALL primes converges. Do you know what it converges to? It converges to: 9 / [2π^2].