  We provide a (simplified) quantum description of primordial black holes at
the time of their formation. Specifically, we employ the horizon quantum
mechanics to compute the probability of black hole formation starting from a
simple quantum mechanical characterization of primordial density fluctuations
given by a Planckian spectrum. We then estimate the initial number of
primordial black holes in the early universe as a function of their typical
mass and temperature of the fluctuation.
