Space density of luminous (log$\frac{L_{\mathrm{X}}}{\mathrm{erg}{\mathrm{s}}^{-1}}=45-46$) and obscured AGNs in gas-rich protocluster cores at z = 4.0 − 4.3 (red circles) computed under two assumptions for the volumes of the structures (see Sect. 4.3), compared with the predictions of AGN X-ray luminosity functions at z = 4.15 in blank fields (Ueda et al. 2014; Georgakakis et al. 2015; Vito et al. 2018b). Gas-rich overdense environments at high redshift enhance the triggering of luminous AGNs by three to five orders of magnitude. This is likely a physical effect, as it appears not to be simply driven by the large number of galaxies in the structures (see Sect. 4.3).