  Primordial black holes (PBHs) are expected to accrete particle dark matter
around them to form ultracompact minihalos (UCMHs), if the PBHs themselves are
not most of the dark matter. We show that if most dark matter is a thermal
relic, then the inner regions of UCMHs around PBHs are highly luminous sources
of annihilation products. Flux constraints on gamma rays and neutrinos set
strong abundance limits, improving previous limits by orders of magnitude.
Assuming enough particle dark matter exists to form UCMHs, we find that
Omega_PBH <~ 10^-4 (for m_DM c^2 ~ 100 GeV) for a vast range in PBH mass. We
briefly discuss the uncertainties on our limits, including those due to the
evolution of the UCMH luminosity as it annihilates.
