Rosser's theorem explained

In number theory, Rosser's theorem states that the

n th prime number is greater than n log n , where log is the natural logarithm function. It was published by J. Barkley Rosser in 1939.^[1]

Its full statement is:

Let

p _{n} be the n th prime number. Then for n\geq 1 p _{n} > n log n.

In 1999, Pierre Dusart proved a tighter lower bound:^[2]

p _{n} > n ( log n + log log n - 1 ).

See also

• Prime number theorem

References

1. Rosser, J. B. "The n -th Prime is Greater than n log n ". Proceedings of the London Mathematical Society 45:21-44, 1939.
2. Pierre Dusart. Dusart. Pierre. The k th prime is greater than k( log k + loglog k - 1 ) for k\geq 2 . Mathematics of Computation. 68. 225. 1999. 411–415. 1620223. 10.1090/S0025-5718-99-01037-6. free.

External links

• Rosser's theorem article on Wolfram Mathworld.