Prime zeta P
From specialfunctionswiki
The prime zeta function is defined by $$P(z) = \displaystyle\sum_{p \mathrm{\hspace{2pt} prime}} \dfrac{1}{p^z},$$ where $\mathrm{Re}(z)>1$. It can be extended outside of this domain via analytic continuation.
Graph of $P(x)$ for $x>1$.
Properties
Relationship between prime zeta, Möbius function, logarithm, and Riemann zeta
