The Asymptotic Binary Goldbach and Lemoine Conjectures

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.