Can primordial black holes be a significant part of dark matter?

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 5×1015 g≲M≲1021 g. This is much less than the mass range coming from the QCD phase transition, allowing the two mechanisms to be easily distinguished.