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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.78.

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The $k^{th}$ prime is greater than $k(\ln k + \ln \ln k-1)$ for $k\geq 2$
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by Pierre Dusart PDF
Math. Comp. 68 (1999), 411-415 Request permission


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 Brent et 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.
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Additional Information
  • Pierre Dusart
  • Affiliation: LACO, ESA 6090, Faculté des Sciences, 123 avenue Albert Thomas, 87060 Limoges Cedex, FRANCE
  • Email:
  • Received by editor(s): June 17, 1996
  • © Copyright 1999 American Mathematical Society
  • Journal: Math. Comp. 68 (1999), 411-415
  • MSC (1991): Primary 11N05; Secondary 11A41
  • DOI:
  • MathSciNet review: 1620223