Rosser's theorem

This article is about a theorem in number theory. For Rosser's technique for proving incompleteness theorems, see Rosser's trick. For Gödel–Rosser incompleteness theorems, see Gödel's incompleteness theorems. For the Church-Rosser theorem of λ-calculus, see Church-Rosser 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:

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

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.