In number theory, Rosser's theorem states that the <math>n</math>th prime number is greater than <math>n \log n </math>, where <math>\log</math> is the natural logarithm function. It was published by J. Barkley Rosser in 1939.
Its full statement is:
Let <math>p_n</math> be the <math>n</math>th prime number. Then for <math>n\geq 1</math>
:<math>p_n > n \log n. </math>
In 1999, Pierre Dusart proved a tighter lower bound:
:<math> p_n > n (\log n + \log \log n - 1). </math>
See also
- Prime number theorem