  We give two extensions of the recent theorem of the first author that the odd
distance graph has unbounded chromatic number. The first is that for any
non-constant polynomial $f$ with integer coefficients and positive leading
coefficient, every finite colouring of the plane contains a monochromatic pair
of distinct points whose distance is equal to $f(n)$ for some integer $n$. The
second is that for every finite colouring of the plane, there is a
monochromatic pair of points whose distance is a prime number.
