  We model the accretion of gas onto a population of massive primordial black
holes in the Milky Way, and compare the predicted radio and X-ray emission with
observational data. We show that under conservative assumptions on the
accretion process, the possibility that ${\cal O}(10) \, M_\odot$ primordial
black holes can account for all of the dark matter in the Milky Way is excluded
at $5\sigma$ by a comparison with a VLA radio catalog at $1.4$ GHz, and at
$\simeq 40\sigma$ by a comparison with a Chandra X-ray catalog ($0.5 - 8$ keV).
We argue that this method can be used to identify such a population of
primordial black holes with more sensitive future radio and X-ray surveys.
