  In this paper we use the former of the authors developed theory of
\textbf{circles of partition} to investigate possibilities to prove the binary
Goldbach as well as the Lemoine conjecture. We state the \textit{squeeze
principle} and its consequences if the set of all odd prime numbers is the base
set. With this tool we can prove asymptotic versions of the binary Goldbach as
well as the Lemoine conjecture.
