Rosser's theorem

In number theory, Rosser's theorem states that the th prime number is greater than , where is the natural logarithm function. It was published by J. Barkley Rosser in 1939.Rosser, J. B. "The -th Prime is Greater than ". Proceedings of the London Mathematical Society 45:21-44, 1939.

Its full statement is:

Let be the th prime number. Then for

In 1999, Pierre Dusart proved a tighter lower bound for :

See also Prime number theorem

References

External links Rosser's theorem article on Wolfram Mathworld.

de:John Barkley Rosser#Satz von Rosser