On the existence of a non-zero lower bound for the number of Goldbach partitions of an even integer

Abstract

The Goldbach partitions of an even number, given by the sums of two prime addends, form the nonempty set for all integers 2n with 2≤n≤2×1014. It will be shown how to determine by the method of induction the existence of a non-zero lower bound for the number of Goldbach partitions of all even integers greater than or equal to 4. The proof depends on contour arguments for complex functions in the unit disk.