# Logarithmic derivative of Riemann zeta in terms of series over primes

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