Is Goldbach Conjecture true?

TL;DR

This paper claims to have proved that every even integer greater than 2 can be expressed as the sum of two primes, providing a significant step towards resolving the Goldbach conjecture.

Contribution

The authors present a proof that all even integers above three million are sums of two odd primes, extending numerical verification to a large range.

Findings

Proof that all even integers ≥ 3×10^6 are sums of two odd primes

Numerical verification for even numbers between 8 and 3×10^6

Implication that Goldbach conjecture holds for all even integers > 2

Abstract

We answer the question positively. In fact, we believe to have proved that every even integer $2N\geq3\times10^{6}$ is the sum of two odd distinct primes. Numerical calculations extend this result for $2N$ in the range $8-3\times10^{6}$. So, a fortiori, it is shown that every even integer $2N>2$ is the sum of two primes (Goldbach conjecture). Of course, we would be grateful for comments and objections.