  A minor-closed class of graphs is a set of labelled graphs which is closed
under isomorphism and under taking minors. For a minor-closed class $C$, we let
$c_n$ be the number of graphs in $C$ which have $n$ vertices. A recent result
of Norine et al. shows that for all minor-closed class $C$, there is a constant
$r$ such that $c_n < r^n n!$. Our main results show that the growth rate of
$c_n$ is far from arbitrary. For example, no minor-closed class $C$ has $c_n=
r^{n+o(n)} n!$ with $0 < r < 1$ or $1 < r < \xi \approx 1.76$.
