# An Elementary Proof of the Binary Goldbach Conjecture

“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.

- Authors: Khaled Qazaqzeh, Aymen Rawashdeh
- Published: November 6, 2026
- Field: Mathematics
- DOI: https://doi.org/10.48550/arxiv.2611.09007
- Free PDF: https://arxiv.org/pdf/2611.09007

## 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].

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