Rosser's theorem

In number theory, Rosser's theorem states that the nth prime number is greater than ${\displaystyle n\ln n}$. It was published by J. Barkley Rosser in 1939.^[1]

Its full statement is:

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

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

In 1999, Pierre Dusart proved a tighter lower bound:^[2]

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

See also[]

• Prime number theorem

References[]

External links[]

• Rosser's theorem article on Wolfram Mathworld.