Has any progress been made since Chen on bounding \begin{equation*} G(n) = \#\{\epsilon N < p_1, p_2 \leq N: n = p_1 - p_2\} \end{equation*} from above?
As far as I can tell, the best upper asymptotic bound we have is still the following from Chen \begin{equation*} G(n) \leq 7.8342\prod_{p \neq 2}\left(1 - \frac{1}{(p - 1)^2}\right)\prod_{\substack{p \mid n\\p > 2}}\left(\frac{p - 1}{p - 2}\right) \frac{N}{(\log N)^2} \end{equation*} where $N$ is allowed to be sufficiently large.
