  Membership identification is the first step to determine 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 with stellar masses $\sim$0.11--2.4 Msun of the intermediate-age
Praesepe cluster (M44), by using Pan-STARRS and 2MASS photometry, and PPMXL
proper motions. Within a sky area of 3 deg radius, 1040 candidates are
identified, of which 96 are new inclusions. Using the same set of selection
criteria on field stars led to an estimate of a false positive rate 16%,
suggesting 872 of the candidates being true members. This most complete and
reliable membership list allows us to favor the BT-Settl model in comparison
with 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.
