SOLVED
Let $A\subseteq \mathbb{N}$ be a set such that $\lvert A\cap \{1,\ldots,N\}\rvert \gg \log N$ for all large $N$. Let $f(n)$ count the number of solutions to $n=p+a$ for $p$ prime and $a\in A$. Is it true that $\limsup f(n)=\infty$?
Erdős
[Er50] proved this when $A=\{2^k : k\geq 0\}$. Solved by Chen and Ding
[ChDi22].
See also [236].
