  The computation of PBH (primordial black hole) production from primordial
perturbations has recently been improved by considering a more accurate
relation between the primordial power spectrum and the PBH mass variance. We
present here exact expressions which are valid for primordial spectra of
arbitrary shape and which allow accurate numerical calculations. We then
consider the possibility to have a significant part of dark matter in the form
of PBHs produced by a primordial spectrum of inflationary origin possessing a
characteristic scale. We show that in this model the relevant PBH mass is
constrained to lie in the range $5\times 10^{15} {\rm g}\lesssim M \lesssim
10^{21} {\rm g}$. This is much less than the mass range coming from the QCD
phase transition, allowing the two mechanisms to be easily distinguished.
