  The emission of particles from black holes created in the early Universe has
detectable astrophysical consequences. The most stringent bound on their
abundance has been obtained from the absence of a detectable diffuse flux of
100 MeV photons. Further scrutiny of these bounds is of interest as they, for
instance, rule out primordial black holes as a dark matter candidate. We here
point out that these bounds can, in principle, be improved by studying the
diffuse cosmic neutrino flux. Measurements of near-vertical atmospheric
neutrino fluxes in a region of low geomagnetic latitude can provide a
competitive bound. The most favorable energy to detect a possible diffuse flux
of primordial black hole origin is found to be a few MeV. We also show that
measurements of the diffuse $\nu _\tau$ flux is the most promising to improve
the existing bounds deduced from gamma-ray measurements. Neutrinos from
individual black hole explosions can be detected in the GeV-TeV energy region.
We find that the kilometer-scale detectors, recently proposed, are able to
establish competitive bounds.
