Verifying the Goldbach conjecture up to \(4\cdot 10^{14}\) (Q2723545)

The author verifies the binary Goldbach conjecture up to \(4{\cdot}10^{14}\) by implementing an optimised segmented sieve and a checking algorithm into a computer program, which was distributed to various workstations. For even \(n\), let \(p(n)\) denote the smallest prime \(p\) for which \(n-p\) is prime. A table for the increasing maximal values of \(p(n)\) is given, showing that \(p(n)/\log^2n\log\log n\) is bounded above by about \(1{\cdot}5\) for the range concerned, with the last entry showing \(p(38996 50268 19938)=5569\). NEWLINENEWLINENEWLINEIn a recent note [\textit{J. Richstein}, Algebraic Number Theory, Leiden 2000, Lect. Notes Comput. Sci. 1838, 475-490 (2000; Zbl 0984.11049)] the range for the number of Goldbach partitions has been extended to \(5.10^8\).