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{{about|a theorem in number theory|Rosser's technique for proving incompleteness theorems|Rosser's trick|Gödel–Rosser incompleteness theorems|Gödel's incompleteness theorems|the Church-Rosser theorem of λ-calculus|Church-Rosser theorem}} | |||
In [[number theory]], '''Rosser's theorem''' was proved by [[J. Barkley Rosser]] in 1938. Its statement follows. | |||
Let ''p''<sub>''n''</sub> be the ''n''th [[prime number]]. Then for ''n'' ≥ 1 | |||
:<math>p_n > n \cdot \ln n. </math> | |||
This result was subsequently improved upon to be: | |||
:<math> p_n > n \cdot(\ln n + \ln(\ln n) - 1). </math> (Havil 2003) | |||
==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. | |||
[[Category:Theorems about prime numbers]] | |||
Revision as of 10:47, 13 July 2013
29 yr old Orthopaedic Surgeon Grippo from Saint-Paul, spends time with interests including model railways, top property developers in singapore developers in singapore and dolls. Finished a cruise ship experience that included passing by Runic Stones and Church.
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:
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.