  Adopting a binned method, we model-independently reconstruct the mass
function of primordial black holes (PBHs) from GWTC-3 and find that such a PBH
mass function can be explained by a broad red-tilted power spectrum of
curvature perturbations. Even though GW190521 with component masses in upper
mass gap $(m>65M_\odot)$ can be naturally interpreted in the PBH scenario, the
events (including GW190814, GW190425, GW200105, and GW200115) with component
masses in the light mass range $(m<3M_\odot)$ are quite unlikely to be
explained by binary PBHs although there are no electromagnetic counterparts
because the corresponding PBH merger rates are much smaller than those given by
LIGO-Virgo. Furthermore, we predict that both the gravitational-wave (GW)
background generated by the binary PBHs and the scalar-induced GWs accompanying
the formation of PBHs should be detected by the ground-based and space-borne GW
detectors and pulsar timing arrays in the future.
