  We study the formation of primordial black holes (PBHs) in the early Universe
during a period of slow reheating after inflation. We demonstrate how the PBH
formation mechanism may change even before the end of the matter-dominated
phase and calculate the expected PBH mass function. We find that there is a
threshold for the variance of the density contrast, $\sigma_c \simeq 0.05$,
below which the transition occurs even before reheating, with this having
important consequences for the PBH mass function. We also show that there is a
maximum cut-off for the PBH mass at around $100\,M_{\odot}$, below which the
subdominant radiation bath affects PBH production, making the scenario
particularly interesting for the recent LIGO observations of black hole
mergers.
