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In number theory, Rosser's theorem was proved by J. Barkley Rosser in 1938. Its statement follows.

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

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

This result was subsequently improved upon to be:

$p_{n}>n\cdot (\ln n+\ln(\ln n)-1).$ (Havil 2003)

See also

• Prime number theorem

References

• Rosser, J. B. "The nth Prime is Greater than n ln n". Proceedings of the London Mathematical Society 45, 21-44, 1938.

External links

• Rosser's theorem article on Wolfram Mathworld.