made available to the community on a public website, can be used for a double purpose: exploiting the rich (and increasing) archive of current X-ray missions; and investigating scientific cases of the next-generation X-ray facilities, in particular those that will perform large-area surveys. Here we do not consider supplementary information, although we may use the CCD spectral information to distinguish thermal (X-ray soft) from nonthermal (X-ray hard) emission. This option is not practical, because mostly the signal-to-noise ratio (S/N) is very low in the hard band (above 2 keV) where the difference between thermal and nonthermal spectra is highest. We also ignore the possibility of cross-correlating X-ray images with images in other wavebands like optical and IR. This process is very effective in finding distant cluster candidates, but it would severely undermine the possibility of clearly defining the surveyed volume, an essential requirement to derive the physical density of the cluster population as a function of the cosmic epoch. Our goal is to obtain samples selected entirely by their X-ray properties and characterized by clearly defined completeness criteria. This requirement is mostly relevant for cosmological tests, where we need a robust estimate of the search volume of the survey to 