# Rosser's theorem

Rosser's theorem For Rosser's technique for proving incompleteness theorems, see Rosser's trick.

In number theory, Rosser's theorem states that the nth prime number is greater than {displaystyle nln n} . It was published by J. Barkley Rosser in 1939.[1] Its full statement is: Let pn be the nth prime number. Then for n ≥ 1 {displaystyle p_{n}>nln n.} In 1999, Pierre Dusart proved a tighter lower bound:[2] {displaystyle p_{n}>n(ln n+ln ln 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. doi:10.1112/plms/s2-45.1.21 ^ Dusart, Pierre (1999). "The kth prime is greater than k(log k + log log k−1) for k ≥ 2". Mathematics of Computation. 68 (225): 411–415. doi:10.1090/S0025-5718-99-01037-6. MR 1620223. External links Rosser's theorem article on Wolfram Mathworld. Categories: Theorems about prime numbers

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