Let us consider the series $\sum_{p\in\Bbb P}{\frac{\log{p}}{p^2-1}}$ where $p$ ranges through prime numbers. We can, using Euler product of Riemann zeta function prove that this series converges to $-\frac{\zeta^\prime(2)}{\zeta(2)}.$ I would like to know whether the limit of series $\sum_{p\in\Bbb P}{\frac{\log{p}}{(p^2-1)^2}}$ where $p$ ranges through prime numbers can be expressed using some values of Riemann zeta function.
Sorry if the question is not written as per community's standards. It is my first question here. Thank you.