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 proved by J. Barkley Rosser in 1938. Its statement follows.
Let pn be the nth prime number. Then for n ≥ 1
This result was subsequently improved upon to be:
(Havil 2003)
See also
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.
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