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 distribu tion is defi 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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Publication Details

Journal
Global Journal of Human Social Science
Published
2025-10-27
DOI
https://doi.org/10.34257/ljrsvol25is12pg29
Primary Topic
Analytic Number Theory Research
Type
article
Field-Weighted Citation Impact
0.00

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article

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

Emilio A. Diarte-Carot
Global Journal of Human Social Science
Analytic Number Theory Research
article

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

Emilio A. Diarte-Carot
article en

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 distribu tion is defi 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.

Global Journal of Human Social Science
Universitat de Girona
Openalex Percentile: Top 58%
Analytic Number Theory Research
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