  We derive constraints on mixed dark-matter scenarios consisting of primordial
black holes (PBHs) and weakly interacting massive particles (WIMPs). In these
scenarios, we expect a density spike of the WIMPs that are gravitationally
bound to the PBHs, which results in an enhanced annihilation rate and increased
indirect detection prospects. We show that such scenarios provide strong
constraints on the allowed fraction of PBHs that constitutes the dark matter,
depending on the WIMP mass $m_{\chi}$ and the velocity-averaged annihilation
cross-section $\langle \sigma v \rangle$. For the standard scenario with
$m_{\chi} = 100\,{\rm GeV}$ and $\langle \sigma v \rangle = 3 \times
10^{-26}\,{\rm cm}^{3} / {\rm s}$, we derive bounds that are stronger than all
existing bounds for PBHs with masses $10^{-12}\,M_{\odot} \lesssim M_{\rm BH}
\lesssim 10^{4}\,M_{\odot}$, where $M_{\odot}$ is the solar mass, and mostly so
by several orders of magnitude.
