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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Verifying the Goldbach conjecture up to $4\cdot 10^{14}$


Author: Jörg Richstein
Journal: Math. Comp. 70 (2001), 1745-1749
MSC (2000): Primary 11P32; Secondary 11-04
Published electronically: July 18, 2000
MathSciNet review: 1836932
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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

DOI: http://dx.doi.org/10.1090/S0025-5718-00-01290-4
PII: S 0025-5718(00)01290-4
Keywords: Goldbach conjecture, distributed computing
Received by editor(s): October 14, 1999
Received by editor(s) in revised form: January 6, 2000
Published electronically: July 18, 2000
Article copyright: © Copyright 2000 American Mathematical Society