A simple verification method for the Goldbach conjecture

Abstract

In class, students are often curious about the fact that any even integer bigger than 4 is the sum of two prime numbers. They usually cannot understand why the obvious fact cannot be proved mathematically. From the computational point of view, unless we find an even number which cannot be expressed as a sum of two prime numbers, we cannot claim the Goldbach conjecture is true. So, the most important thing is to try all the even integers to check if they conform to the Goldbach conjecture. Unfortunately, most of the modern verification methods need deep mathematical ideas which usually cannot be understood by undergraduate students. In this paper, we present a simple but elegant computer verification method for the Goldbach conjecture, and propose two implementation approaches (via C and Maple) to this method. Compared with other verification methods, ours is easy to implement and easy to understand. But of course, at present we may not expect this method, or probably any other existing methods, to be able...