Checking the Goldbach conjecture up to 4⋅10¹¹

Abstract

One of the most studied problems in additive number theory, Goldbach’s conjecture, states that every even integer greater than or equal to 4 can be expressed as a sum of two primes. In this paper checking of this conjecture up to 4 ⋅ 10 11 4 \cdot {10^{11}} by the IBM 3083 mainframe with vector processor is reported.