Prime zeta function

In mathematics, the prime zeta function is an analogue of the Riemann zeta function, studied by Glaisher (1891). It is defined as the following infinite series, which converges for ${\displaystyle \Re (s)>1}$:

${\displaystyle P(s)=\sum _{p\,\in \mathrm {\,primes} }{\frac {1}{p^{s}}}={\frac {1}{2^{s}}}+{\frac {1}{3^{s}}}+{\frac {1}{5^{s}}}+{\frac {1}{7^{s}}}+{\frac {1}{11^{s}}}+\cdots .}$