Can $(x-1)(y+1)+xy$ be a Fermat-pseudoprime , when $x$ is a power of $2$ and $y$ a power of $10$?

Question

Suppose, $m$ and $n$ are positive integers and $x=2^m$ and $y=10^n$.

Can $$(x-1)(y+1)+xy$$ be a Fermat-pseudoprime to base $2$ ?

For $m,n\le 200$, no such Fermat-pseudoprime exists.