Definitive Proof of Goldbach's conjecture
Abstract
The Goldbach conjecture states that every even integer greater than 2 can be expressed as the sum of two prime numbers. This conjecture was first proposed by German mathematician Christian Goldbach in 1742 and, despite being obviously true, has remained unproven. In this paper, it is shown that the set of all even integers n that are not divisible by a prime number less than the square root of n has the relatively fewest number of prime pairs. An equation was derived that approximates the number of prime pairs for these values of n. It was then proven that this equation never goes to zero for any n, and as n increases, the number of prime pairs also increases, thus validating Goldbach's conjecture. Error analysis was performed to show that the difference between this approximation and the actual number of prime pairs is small enough so that for all n > 622, the number of prime pairs of n is greater than 1, thus proving Goldbach's conjecture.
Cite
@article{arxiv.1811.02415,
title = {Definitive Proof of Goldbach's conjecture},
author = {Kenneth A. Watanabe},
journal= {arXiv preprint arXiv:1811.02415},
year = {2025}
}
Comments
27 pages, 6 figures. The following modifications were made from the previous version - the W(n) function was simplified to be the fraction of prime pairs less than n, proof was modified to take into account the new W(n) function, error analysis was performed to confirm deviation from actual prime pair counting function was small, figures were added to further explain proof