Some discussions on the Goldbach conjecture

TL;DR

This paper discusses various aspects of the Goldbach conjecture, including weaker results, sufficient conditions, and related conjectures, aiming to deepen understanding of this longstanding mathematical problem.

Contribution

It presents new results weaker than the Goldbach conjecture, establishes sufficient conditions, and explores connections with other famous conjectures.

Findings

Identification of results weaker than Goldbach conjecture

Derivation of sufficient conditions for Goldbach conjecture

Analysis of relationships between Goldbach and other conjectures

Abstract

According to some discussions based on syllogism, we present results on the binary Goldbach conjecture in three categories: results that are weaker than the Goldbach conjecture, sufficient conditions for the Goldbach conjecture, and results that are similar in nature to the Goldbach conjecture. Additionally, we explore the connections between the Goldbach conjecture and other well-known conjectures.