Membership identification is the first step in determining the properties of a star cluster. Low-mass members in particular could be used to trace the dynamical history, such as mass segregation, stellar evaporation, or tidal stripping, of a star cluster in its Galactic environment. We identified member candidates of the intermediate-age Praesepe cluster (M44) with stellar masses ~0.11-2.4 M ☉, using Panoramic Survey Telescope And Rapid Response System and Two Micron All Sky Survey photometry, and PPMXL proper motions. Within a sky area of 3° radius, 1040 candidates are identified, of which 96 are new inclusions. Using the same set of selection criteria on field stars, an estimated false positive rate of 16% was determined, suggesting that 872 of the candidates are true members. This most complete and reliable membership list allows us to favor the BT-Settl model over other stellar models. The cluster shows a distinct binary track above the main sequence, with a binary frequency of 20%-40%, and a high occurrence rate of similar mass pairs. The mass function is consistent with that of the disk population but shows a deficit of members below 0.3 solar masses. A clear mass segregation is evidenced, with the lowest-mass members in our sample being evaporated from this disintegrating cluster.