On a prime summation
Posted: Wed Sep 13, 2017 8:46 am
Let $p_n$ denote the $n$ -th prime number. Evaluate the sum
$$\mathcal{S} = \sum_{n=1}^{\infty} \frac{ \log p_n}{p_n^2 -1}$$
$$\mathcal{S} = \sum_{n=1}^{\infty} \frac{ \log p_n}{p_n^2 -1}$$