Primes Product, or Sum??

Relevant wiki: Prime Zeta Function

$\begin{aligned} P & = \prod_{\color{#3D99F6}k=2}^\infty \frac {p_k^2}{p_k^2-1} & \small \color{#3D99F6} \text{where }p_k \text{ is the }k\text{th prime.} \\ & = \frac {2^2-1}{2^2} \prod_{\color{#D61F06}k=1}^\infty \frac {p_k^2}{p_k^2-1} \\ & = \frac 34 \color{#3D99F6} \prod_{k=1}^\infty \frac 1{1- p_k^{-2}} & \small \color{#3D99F6} \text{By Euler product }\zeta (s) = \prod_{k=1}^\infty \left(1-\frac 1{p_k^s}\right)^{-1} \\ & = \frac 34 \color{#3D99F6} \zeta (2) & \small \color{#3D99F6} \text{where }\zeta (\cdot) \text{ is the Riemann zeta function.} \\ & = \frac 34 \left({\color{#3D99F6} \frac {\pi^2}6}\right) & \small \color{#3D99F6} \text{see reference: } Prime\ Zeta\ Function. \\ & = \frac {\pi^2}8 \approx \boxed{1.234} \end{aligned}$

$\begin{aligned}\prod_{p\in P}\dfrac{p^2}{p^2-1}&=\prod_{p\in P}\dfrac{1}{1-1/p^2}\\&=\bigg(1+\frac19+\frac1{81}+\dots\bigg)\bigg(1+\dfrac1{25}+\dfrac1{625}+\dots\bigg)...\\&=1+\dfrac1{3^2}+\dfrac1{5^2}+\dfrac1{7^2}+\dfrac1{9^2}+\dfrac1{11^2}+\dots\\&=\zeta(2)-\dfrac14\zeta(2)\\&=\dfrac34\cdot\dfrac{\pi^2}6\\&=\boxed{\dfrac{\pi^2}{8}}\end{aligned}$