Relation between the value of L₅₀₀, M₅₀₀, F₅₀₀, and the integrated cluster numbers with larger luminosity, mass, or flux. Bottom-left panel: the dashed line has a slope of −1.5, normalized to match the value with f_X = 2 × 10⁻¹¹ erg s⁻¹ cm⁻². The dotted vertical line labels the flux of 5 × 10⁻¹² erg s⁻¹ cm⁻². Bottom-right panel: relation between the redshift and L₅₀₀. The curves for the flux limits of 10⁻¹² and 3 × 10⁻¹² erg s⁻¹ cm⁻² are overlapped as dotted curve and dashed curve, respectively. Both the F₅₀₀ and L₅₀₀ are the value in [0.1−2.4] keV band.