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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.

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.


Computing prime harmonic sums
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by Eric Bach, Dominic Klyve and Jonathan P. Sorenson PDF
Math. Comp. 78 (2009), 2283-2305 Request permission


We discuss a method for computing $\sum _{p \le x} 1/p$, using time about $x^{2/3}$ and space about $x^{1/3}$. It is based on the Meissel-Lehmer algorithm for computing the prime-counting function $\pi (x)$, which was adapted and improved by Lagarias, Miller, and Odlyzko. We used this algorithm to determine the first point at which the prime harmonic sum first crosses 4.
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Additional Information
  • Eric Bach
  • Affiliation: Computer Sciences Department, University of Wisconsin-Madison, 1210 W. Dayton Street, Madison, Wisconsin 53706
  • Email:
  • Dominic Klyve
  • Affiliation: Department of Mathematics, Carthage College, 2001 Alford Drive, Kenosha, Wisconsin 53140
  • MR Author ID: 776121
  • Email:
  • Jonathan P. Sorenson
  • Affiliation: Computer Science and Software Engineering, Butler University, Indianapolis, Indiana 46208
  • MR Author ID: 334195
  • Email:
  • Received by editor(s): June 19, 2008
  • Received by editor(s) in revised form: November 28, 2008
  • Published electronically: April 3, 2009
  • Additional Notes: E. Bach was supported by NSF grants CCR-0523680, CCF-0635355, and a Vilas Associate Award from the Wisconsin Alumni Research Foundation.
    D. Klyve was supported by NSF grant DMS-0401422
    J. P. Sorenson was supported by a grant from the Holcomb Awards Committee
    A preliminary version of this work was presented as a poster at ANTS-VII in Berlin, Germany, July 2006.
  • © Copyright 2009 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Math. Comp. 78 (2009), 2283-2305
  • MSC (2000): Primary 11Y16; Secondary 11Y35, 11N05, 68Q25
  • DOI:
  • MathSciNet review: 2521290