# Variant on PrimeZetaP

Mathematica has PrimeZetaP for the prime zeta function $$\sum_p \frac{1}{p^s}$$ where the sum is taken over all primes.

How do I use Mathematica to make an equivalent summation that runs over all primes that are plus or minus 6 from another prime? In other words,

$$\sum_{{q,q\pm 6}\in\mathbb{P}} \frac{1}{q^s}$$

• Only that the sum converges to Brun’s constant which lies somewhere between (roughly) $1.8$ and $2.4$. – Richard Burke-Ward Feb 6 at 0:24