Remote Access Mathematics of Computation
Green Open Access

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information


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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC (2000): 11P32, 11-04

Retrieve articles in all journals with MSC (2000): 11P32, 11-04

Additional Information

Jörg Richstein
Affiliation: Institut für Informatik, Fachbereich Mathematik, Justus-Liebig-Universität, Gies- sen, Germany

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