TITLE: Is $ 5 $ the only number that cannot be expressed as $ p + x ^ y$?
QUESTION [5 upvotes]: Let $n,x,y \in \mathbb{N}$ where $n\ge3,y\ge2$ and $p$ is prime number.
For some $n$, $n$ can be expressed as $n=p+x^y$
Example
$3=2+1^y$
$15=7+2^3$
We can check, $5$ can't be expressed.

Question

Is $ n=5 $ the only number that cannot be expressed as $ p + x ^ y$ ?


I checked, there are always pair for n=3 up to n = 50. Except $5$.

REPLY [4 votes]: According to OEIS, other such numbers include 1549 and 1771561. It is apparently unknown whether there are any more.