Top left panel: integral number of radio mini-halo candidates (3π sr) observable at 140 MHz by LOFAR (triangles) and SKA1-LOW (circles), and at 1.4 GHz by SKA1-MID (squares) as a function of redshift, estimated by assuming two reference values of B =  1 μG (blue) and B =  30 μG (red). The error bars indicate the 1σ uncertainty driven by the P_radio − L_X correlation (Eq. (4)). Top right panel: differential number of radio mini-halo candidates (3π sr) observable at 1.4 GHz by SKA1-MID in different redshift bins, estimated by assuming three reference values of B =  1 μG (blue), B =  10 μG (black), and B =  30 μG (red). The vertical error bars indicate the 1σ uncertainty driven by the P_radio − L_X correlation (Eq. (4)), and the horizontal bars indicate the size of the redshift bin. The points corresponding to the three different B-field values in the same redshift bin are slightly shifted on the x-axis to improve clarity. Bottom left panel: same as top right panel, but showing the results for LOFAR at 140 MHz. Bottom right panel: same as top right panel, but showing the results for SKA1-LOW at 140 MHz.