${\sum }_{p\le n}1/p=\ln (\ln n)+O(1)$: An Exposition

William Gasarch, Larry Washington

It is well known that ${\sum }_{p\le n}1/p=\ln (\ln (n))+O(1)$ where $p$ goes over the primes. We give several known proofs of this. We first present a a proof that $\ge \ln(\ln(n))…