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

Let *p*_{n} be the *n*th prime number. Then for *n* ≥ 1

p
n
>
n
⋅
ln
n
.
This result was subsequently improved upon to be:

p
n
>
n
⋅
(
ln
n
+
ln
(
ln
n
)
−
1
)
.
(Havil 2003)