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arXiv · 2611.09007

An Elementary Proof of the Binary Goldbach Conjecture

Khaled Qazaqzeh·Aymen Rawashdeh
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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 $\mathcal{O}\left(\frac{n}{\ln^{2} n}\right)$ function. As an application, we provide a simpler verification of the ternary Goldbach conjecture that was first established in [6,7].

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Khaled Qazaqzeh, Aymen Rawashdeh. 2026-11-06. An Elementary Proof of the Binary Goldbach Conjecture. https://arxiv.org/abs/2611.09007

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