Rosser's theorem

Rosser's theorem

:"This article is about a theorem in number theory. For the Gödel–Rosser incompleteness theorems, see Gödel's incompleteness theorems and Rosser's trick."

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

Let "P""n" be the "n"th prime number. Then for "n" > 1

:"P""n" > "n" ln "n".

See also

* Prime number theorem

References

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

External links

* [http://mathworld.wolfram.com/RossersTheorem.html Rosser's theorem] article on Wolfram Mathworld.


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