Rosser's theorem

In number theory, Rosser's theorem states that the $n$th prime number is greater than $n\log n$, where $\log$ is the natural logarithm function. It was published by J. Barkley Rosser in 1939.

Its full statement is:

Let $p_n$ be the $n$th prime number. Then for $n\ge 1$

$p_n>n\log n.$

In 1999, Pierre Dusart proved a tighter lower bound for $n\ge 2$:

$p_n>n(\log n+\log \log n-1).$

See also

• Prime number theorem

External links

• Rosser's theorem article on Wolfram Mathworld.