Series for log(riemann zeta) over primes

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.

References

• 1930: Edward Charles Titchmarsh: The Zeta-Function of Riemann ... (previous) ... (next): § Introduction $(2')$