The Asymptotic Binary Goldbach and Lemoine Conjectures

TL;DR

This paper employs a novel theory of circles of partition and the squeeze principle to establish asymptotic versions of the binary Goldbach and Lemoine conjectures.

Contribution

It introduces the squeeze principle and applies it to prove asymptotic forms of two longstanding conjectures in number theory.

Findings

Proved asymptotic binary Goldbach conjecture.

Proved asymptotic Lemoine conjecture.

Developed the theory of circles of partition.

Abstract

In this paper, we use the former of the authors developed theory of \emph{circles of partition} to investigate possibilities to prove the binary Goldbach and Lemoine conjectures. We state the \emph{squeeze principle} and its consequences when the set of all odd prime numbers is the base set. Using this tool, we can prove asymptotic versions of the binary Goldbach and the Lemoine conjecture.