The binary Goldbach conjecture is also true

TL;DR

This paper proves the binary Goldbach conjecture by estimating a key integer threshold, showing that every even number greater than a certain bound can be expressed as the sum of two primes.

Contribution

It provides an estimation for the threshold beyond which the Goldbach conjecture holds, thereby proving the conjecture.

Findings

The binary Goldbach conjecture is proven to be true.

A specific bound for the conjecture's validity is established.

Every even integer greater than this bound can be expressed as the sum of two primes.

Abstract

The binary Goldbach conjecture asserts that every even integer greater than $4$ is the sum of two primes. In a preceding paper we have proved that there exists a positive integer $K_\alpha$ such that every even integer $x > p_k^2$ can be expressed as the sum of two primes, where $p_k$ is the $k$th prime number and $k > K_\alpha$. In this paper we provide an estimation for $K_\alpha$, and from this result it follows that the binary Goldbach conjecture is true.