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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.


On the greatest prime factor of $p-1$ with effective constants
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by G. Harman PDF
Math. Comp. 74 (2005), 2035-2041 Request permission


Let $p$ denote a prime. In this article we provide the first published lower bounds for the greatest prime factor of $p-1$ exceeding $(p-1)^{\frac 12}$ in which the constants are effectively computable. As a result we prove that it is possible to calculate a value $x_0$ such that for every $x > x_0$ there is a $p < x$ with the greatest prime factor of $p-1$ exceeding $x^{\frac 35}$. The novelty of our approach is the avoidance of any appeal to Siegel’s Theorem on primes in arithmetic progression.
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Additional Information
  • G. Harman
  • Affiliation: Department of Mathematics, Royal Holloway University of London, Egham, Surrey TW20 0EX, United Kingdom
  • Email:
  • Received by editor(s): March 19, 2004
  • Received by editor(s) in revised form: August 16, 2004
  • Published electronically: February 16, 2005
  • © Copyright 2005 American Mathematical Society
  • Journal: Math. Comp. 74 (2005), 2035-2041
  • MSC (2000): Primary 11N13
  • DOI:
  • MathSciNet review: 2164111