Solving Goldbach’s Conjecture using Gaussian Arithmetic and a Probabilistic Model

This paper proves that Goldbach’s conjecture is true.  The proof uses Gaussian modular arithmetic to calculate the number of pairs of odd numbers, KT , whose sum is a given even  number, n, as well as, the number, KE, of those that can potentially contain prime numbers. Next, a probabilistic model with a binomial probability distribution is de ned, which will be applied to KE to calculate a function f(x) for the expected value, E(X), where X is the number of pairs formed by two prime numbers. Finally, the analysis of this function, f(x), will allow us to prove that the conjecture is true.

The authors declare no conflict of interest.

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The datasets used in this study are openly available at [repository link] and the source code is available on GitHub at [GitHub link].

This work did not receive any external funding.