OPEN
Let $C>1$. Does the set of integers of the form $p+\lfloor C^k\rfloor$, for some prime $p$ and $k\geq 0$, have density $>0$?
Originally asked to Erdős by Kalmár. Erdős believed the answer is yes. Romanoff
[Ro34] proved that the answer is yes if $C$ is an integer.
