Goldbach's Racetrack

TL;DR

This paper proposes a new approach to prove Goldbach's conjecture by analyzing a function estimating Goldbach pairs, showing the estimate improves with larger even integers and the error remains small.

Contribution

It introduces a novel function and framework that could potentially lead to a proof of Goldbach's conjecture by examining pair estimates and error bounds.

Findings

Estimate of Goldbach pairs increases with even integers

Error term in the estimate remains small

Framework suggests potential for a proof of the conjecture

Abstract

The Goldbach conjecture that, every even integer is the sum of two primes, has been open since 1742. This paper details a road map to a proof of Goldbachs conjecture based on a function that estimates the number of Goldbach pairs. It is shown that the estimate of the number of Goldbach pairs increases as the even integer increases and that the error term is small. Further detailing the functions, assumptions and error term may finally lead to a proof of Goldbachs conjecture.