Series for log(riemann zeta) over primes

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Theorem

The following formula holds: $$\log \left( \zeta(z) \right)=\displaystyle\sum_{p \hspace{2pt} \mathrm{prime}} \displaystyle\sum_{k=1}^{\infty} \dfrac{1}{kp^{mz}},$$ where $\log$ denotes the logarithm and $\zeta$ denotes the Riemann zeta.

Proof

References