Goldbach's Function Approximation Using Deep Learning

TL;DR

This paper introduces a deep learning model that predicts the number of Goldbach partitions for even numbers, outperforming traditional estimations without prime factorization, marking a novel approach in number theory research.

Contribution

It is the first to apply machine learning to approximate solutions for an open problem in number theory, specifically Goldbach's conjecture.

Findings

Model outperforms state-of-the-art estimations

Does not require prime factorization

Advances data-driven approaches in mathematical conjectures

Abstract

Goldbach conjecture is one of the most famous open mathematical problems. It states that every even number, bigger than two, can be presented as a sum of 2 prime numbers. % In this work we present a deep learning based model that predicts the number of Goldbach partitions for a given even number. Surprisingly, our model outperforms all state-of-the-art analytically derived estimations for the number of couples, while not requiring prime factorization of the given number. We believe that building a model that can accurately predict the number of couples brings us one step closer to solving one of the world most famous open problems. To the best of our knowledge, this is the first attempt to consider machine learning based data-driven methods to approximate open mathematical problems in the field of number theory, and hope that this work will encourage such attempts.