PHZ number counts at 353 GHz (red squares), compared to the “clumps” number counts analytical predictions of Negrello et al. (2005) for three assumptions of the amplitude of the 3-point correlation function, Q, (i.e., Q = 1, Q = 1 /b, and Q = 1 /b², where b is the clustering bias parameter). Two cases of the PHZ number counts are presented, depending on the assumption made about the intrinsic number of clumps composing the PHZ source: n = 1 (red); and n = 3 (orange). The blue diamond gives the number counts estimate reported by Clements et al. (2014) for proto-cluster candidates selected from the Planck ERCSC catalogue. The vertical dash-dot-dot-dotted lines provide the 80% completeness limit of the PHZ catalogue at 353 GHz, estimated from MCQA simulations.