Verifying the Goldbach conjecture up to 4⋅10¹⁴

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 ⋅ 10 14 4\cdot 10^{14} . The program was distributed to various workstations. It kept track of maximal values of the smaller prime p p in the minimal partition of the even numbers, where a minimal partition is a representation 2 n = p + q 2n = p + q with 2 n − p ′ 2n - p’ being composite for all p ′ > p p’ > p . The maximal prime p p needed in the considered interval was found to be 5569 and is needed for the partition 389965026819938 = 5569 + 389965026814369.