Number of MAMBO proto-clusters and the sky-filling factor in a Δ_{z (50%)} redshift interval as a function of redshift and proto-cluster mass limit. The numbers are only shown for the sample with M_pc ≥ 10¹⁴ M_⊙ as a dotted line. Solid lines show the fraction of the sky covered by the proto-clusters, and the dashed lines display the combined sky area of the proto-clusters. The thick lines with larger data points show the results for the core regions, while the thin lines show those for the region out to r_pc. For the core regions of the M_pc ≥ 3 × 10¹⁴ M_⊙ proto-clusters, the dashed and solid lines overlap.