Solving Goldbach’s Conjecture using Gaussian Arithmetic and a Probabilistic Model
DOI:
https://doi.org/10.34257/LJRSVOL25IS12PG29Keywords:
relativity., Special Theory of Relativity, Einstein, reference body., Energy, Zero, cosmic origin, information and matter, force, thermodynamics and existence.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.
References
Christian Goldbach (1742) Letter to Leonhard Euler, Moscow, June 7, 1742.
T. Oliveira e Silva, S. Herzog, Silvio Pardi (2014) Empirical Verication of the Even Goldbach Conjecture and Computation of Prime Gaps up to 4 x 10^18. 83(288), 2033-2060.
A. Farhadian (2025) Goldbach Conjecture: Violation Probability and Generalization to Prime-like Distributions. https://arxiv.org/abs/2504.14353v1
Carl Friedrich Gauss (1965) Disquisitiones Arithmeticae.
E. A. Diarte-Carot (2025) Solving the Collatz Conjecture, Using Gaussian Arith-metric.. 13, 1960-1968. https://doi.org/10.4236/jamp.2025.135109
James Glyn, D. Burley, D. Clements, P. Dyke, J. Searl, J. Wright (1996) Modern Engineering Mathematics 2nd Edition. 873-874.
P. L. Meyer (1970) Introductory Probability and Statistical Aplieds. 64 and 12.
Carl Friedrich Gauss (1863) Werke. 2, 444-447.
James Stewart (2008) Calculus: Early Transcendents (6a edicion). 273.
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