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.
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.