Dr. Emilio a. Diarte-Carot

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

Introduction

Solving goldbach's conjecture using gaussian arithmetic and a probabilistic model. This paper proves Goldbach's Conjecture true using Gaussian modular arithmetic to count odd number pairs and a probabilistic model to determine prime number pairs.

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.

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