  Observational constraints on gamma rays produced by the annihilation of
weakly interacting massive particles around primordial black holes (PBHs) imply
that these two classes of Dark Matter candidates cannot coexist. We show here
that the successful detection of one or more PBHs by radio searches (with the
Square Kilometer Array) and gravitational waves searches (with LIGO/Virgo and
the upcoming Einstein Telescope) would set extraordinarily stringent
constraints on virtually all weak-scale extensions of the Standard Model with
stable relics, including those predicting a WIMP abundance much smaller than
that of Dark Matter. Upcoming PBHs searches have in particular the potential to
rule out almost the entire parameter space of popular theories such as the
minimal supersymmetric standard model and scalar singlet Dark Matter.
