“An Elementary Proof of the Binary Goldbach Conjecture” (2026), by Khaled Qazaqzeh et al. Mathematics research paper. Original abstract below, unchanged. A free PDF is available.

An Elementary Proof of the Binary Goldbach Conjecture

Khaled Qazaqzeh, Aymen Rawashdeh · November 6, 2026 · Mathematics

Abstract

We establish the binary Goldbach conjecture which asserts that every even positive integer greater than four can be expressed as a sum of two odd primes. This goal is achieved by proving that the number of ordered Goldbach pairs that add up to 2n is an O(n/ln² n) function. As an application, we provide a simpler verification of the ternary Goldbach conjecture that was first established in [6,7].

Free PDF DOI: 10.48550/arxiv.2611.09007