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Proceedings of the American Mathematical Society Series B

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society Series B (BPROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 2330-1511

The 2020 MCQ for Proceedings of the American Mathematical Society Series B is 0.84.

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.

 

The Erdős conjecture for primitive sets
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by Jared Duker Lichtman and Carl Pomerance HTML | PDF
Proc. Amer. Math. Soc. Ser. B 6 (2019), 1-14

Abstract:

A subset of the integers larger than 1 is primitive if no member divides another. Erdős proved in 1935 that the sum of $1/(a\log a)$ for $a$ running over a primitive set $A$ is universally bounded over all choices for $A$. In 1988 he asked if this universal bound is attained for the set of prime numbers. In this paper we make some progress on several fronts and show a connection to certain prime number “races” such as the race between $\pi (x)$ and $\mathrm {li}(x)$.
References
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Additional Information
  • Jared Duker Lichtman
  • Affiliation: Department of Mathematics, Dartmouth College, Hanover, New Hampshire 03755
  • MR Author ID: 1237291
  • Email: jdl.18@dartmouth.edu, jared.d.lichtman@gmail.com
  • Carl Pomerance
  • Affiliation: Department of Mathematics, Dartmouth College, Hanover, New Hampshire 03755
  • MR Author ID: 140915
  • Email: carl.pomerance@dartmouth.edu
  • Received by editor(s): June 6, 2018
  • Received by editor(s) in revised form: June 26, 2018, August 3, 2018, and August 14, 2018
  • Published electronically: April 10, 2019
  • Additional Notes: The first-named author is grateful for support from the office of undergraduate research at Dartmouth College.
  • Communicated by: Amanda Folsom
  • © Copyright 2019 by the authors under Creative Commons Attribution-Noncommercial 3.0 License (CC BY NC 3.0)
  • Journal: Proc. Amer. Math. Soc. Ser. B 6 (2019), 1-14
  • MSC (2010): Primary 11B83; Secondary 11A05, 11N05
  • DOI: https://doi.org/10.1090/bproc/40
  • MathSciNet review: 3937344