"nice" primes (primes $p$, such that $\pi(p)$ is prime as well) are introduced.
Is it known whether the sum of the reciprocals of the nice primes is convergent ?
The sum of the reciprocals of the primes in an arithmetic progression $an+b$ , where $a$ and $b$ are coprime and $n$ runs over the natural numbers, is divergent.
Intuitively, I would expect that there should exist enough nice primes to get a divergent series, but I may be wrong.
Has anyone an idea or a reference ?