Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



The $k^{th}$ prime is greater than
$k(\ln k +\ln\ln k -1)$ for $k\geq 2$

Author: Pierre Dusart
Journal: Math. Comp. 68 (1999), 411-415
MSC (1991): Primary 11N05; Secondary 11A41
MathSciNet review: 1620223
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: ROSSER and SCHOENFELD have used the fact that the first 3,500,000 zeros of the RIEMANN zeta function lie on the critical line to give estimates on $\psi(x)$ and $\theta(x)$. With an improvement of the above result by BRENTet al., we are able to improve these estimates and to show that the $k^{th}$ prime is greater than $k(\ln k +\ln\ln k -1)$ for $k\geq 2$. We give further results without proof.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC (1991): 11N05, 11A41

Retrieve articles in all journals with MSC (1991): 11N05, 11A41

Additional Information

Pierre Dusart
Affiliation: LACO, ESA 6090, Faculté des Sciences, 123 avenue Albert Thomas, 87060 Limoges Cedex, FRANCE

Keywords: Distribution of primes, arithmetic functions
Received by editor(s): June 17, 1996
Article copyright: © Copyright 1999 American Mathematical Society