Rosser's theorem

In number theory, Rosser's theorem was published by J. Barkley Rosser in 1939. Its statement follows.

Let p_n be the nth prime number. Then for n ≥ 1

${\displaystyle p_{n}>n\cdot \ln n.}$

This result was subsequently improved upon to be[1]:

${\displaystyle p_{n}>n\cdot (\ln n+\ln(\ln n)-1).}$