  We analyze the detection prospects for potential Primordial Black Hole Binary
(PBHB) populations buried in the Stellar-Origin Black Hole Binary (SOBHB)
population inferred by the LVK collaboration. We consider different PBHB
population scenarios and several future Gravitational Wave (GW) detectors. To
separate the PBHB component from the SOBHB one, we exploit the prediction that
the PBHB merger rate does not decline as fast as the SOBHB one at high
redshift. However, only a tiny fraction of PBHB events may be resolved
individually, and the sub-threshold events may yield an undetectable Stochastic
GW Background (SGWB). For this reason, we determine the statistical
significance of the PBHB contributions in the number of resolvable events seen
in future Earth-based detectors and the SGWB measured at LISA. We find that the
synergy between these probes will consistently help assess whether or not a
sizeable PBHB population is present.
