I know that $\sum_{p\in\mathbb{P}} \frac{1}{p^s}$ (s>1) converges. Now, I define $J(s) = \sum_{p\in\mathbb{P}} \frac{1}{p^s}$. Are there any "well known" values for J(2),J(3),J(4), etc? like we all know that $\zeta(2)= \frac{\pi^2}{6}$, $\zeta(4)=\frac{\pi^4}{90}$, etc.