Skip to Main Content

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.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


A still sharper region where $\pi (x)-{\mathrm {li}}(x)$ is positive
HTML articles powered by AMS MathViewer

by Yannick Saouter, Timothy Trudgian and Patrick Demichel PDF
Math. Comp. 84 (2015), 2433-2446 Request permission


We consider the least number $x$ for which a change of sign of $\pi (x)-\mathrm {li}(x)$ occurs. First, we consider modifications of Lehman’s method that enable us to obtain better estimates of some error terms. Second, we establish a new smaller upper bound for the first $x$ for which the difference is positive. Third, we use numerical computations to improve the final result.
Similar Articles
Additional Information
  • Yannick Saouter
  • Affiliation: Institut Telecom Brest, Department Informatique, CS 83818, 29238 Brest, Cedex 3 France
  • Email:
  • Timothy Trudgian
  • Affiliation: The Australian National University, Mathematical Sciences Institute, Building 27, ACTON, ACT 0200 Australia
  • MR Author ID: 909247
  • Email:
  • Patrick Demichel
  • Affiliation: Hewlett-Packard France, 91947 Les Ulis, Cedex France
  • Email:
  • Received by editor(s): June 11, 2013
  • Received by editor(s) in revised form: December 4, 2013
  • Published electronically: February 12, 2015
  • Additional Notes: The second author was supported in part by ARC Grant DE120100173.
  • © Copyright 2015 American Mathematical Society
  • Journal: Math. Comp. 84 (2015), 2433-2446
  • MSC (2010): Primary 11-04, 11A15, 11M26, 11Y11, 11Y35
  • DOI:
  • MathSciNet review: 3356033