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

Abstract

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.