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

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 n-th Prime is Greater than n log n". Proceedings of the London Mathematical Society 45, 21-44, 1939.

External links

Rosser's theorem article on Wolfram Mathworld.

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