$ \sum_{p } \sum_{k=2}^{\infty} \frac{\log p}{p^k}$ is Convergent

Question

How can I show the sum $ \sum_{p } \sum_{k=2}^{\infty} \frac{\log p}{p^k}$ where $p$ varies over all the primes, is Convergent?

I tried comparing with the convergent series $\sum_{p} \frac{1}{p^2}$, but it doesn't seem to work.

Any help would be appreciated. Thanks in advance.