RH implies prime number theorem

Question

I have heard that it is easy to show the prime number theorem using the Riemann hypothesis (RH implies PNT). I have also heard that the prime number theorem is equivalent to the (shown) fact that the zeros of $\zeta$ lie outside of $\text{Re}(z) = 1$.

This is very interesting, but I can't seem to find a proof, let alone the nicest one. Maybe someone has a link?

Answer 1

Have a look at https://arxiv.org/pdf/1609.02301.pdf and https://www.claymath.org/sites/default/files/ezeta.pdf about Riemann's original paper.