Rosser's theorem

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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

↑ Rosser, J. B. "The $n$ -th Prime is Greater than $n \log n$ ". Proceedings of the London Mathematical Society 45:21-44, 1939. Script error: No such module "doi".Template:Closed access
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External links

Rosser's theorem article on Wolfram Mathworld.

de:John Barkley Rosser#Satz von Rosser

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