  The non-observation of Hawking radiation from primordial black holes of
$10^{16}$g sets a conservative strong bound on their cosmological abundance. We
revisit this bound and show how it can be improved (both in mass reach and
strength) by an adequate modeling of the combined AGN and blazar emission in
the MeV range. We also estimate the sensitivity to the primordial black hole
abundance of a future X-ray experiment capable of identifying a significantly
larger number of astrophysical sources contributing to the diffuse background
in this energy range.
