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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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Verifying the Goldbach conjecture up to $4\cdot 10^{14}$
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by Jörg Richstein PDF
Math. Comp. 70 (2001), 1745-1749 Request permission

Abstract:

Using a carefully optimized segmented sieve and an efficient checking algorithm, the Goldbach conjecture has been verified and is now known to be true up to $4\cdot 10^{14}$. The program was distributed to various workstations. It kept track of maximal values of the smaller prime $p$ in the minimal partition of the even numbers, where a minimal partition is a representation $2n = p + q$ with $2n - p’$ being composite for all $p’ < p$. The maximal prime $p$ needed in the considered interval was found to be 5569 and is needed for the partition 389965026819938 = 5569 + 389965026814369.
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Additional Information
  • Jörg Richstein
  • Affiliation: Institut für Informatik, Fachbereich Mathematik, Justus-Liebig-Universität, Gies- sen, Germany
  • Email: Joerg.Richstein@informatik.uni-giessen.de
  • Received by editor(s): October 14, 1999
  • Received by editor(s) in revised form: January 6, 2000
  • Published electronically: July 18, 2000
  • © Copyright 2000 American Mathematical Society
  • Journal: Math. Comp. 70 (2001), 1745-1749
  • MSC (2000): Primary 11P32; Secondary 11-04
  • DOI: https://doi.org/10.1090/S0025-5718-00-01290-4
  • MathSciNet review: 1836932