Studies of the mass function (MF) of open clusters of different ages allow us to probe the efficiency with which brown dwarfs (BDs) are evaporated from clusters to populate the field. Surveys in old clusters (age gtrsim 100 Myr) do not suffer so severely from several problems encountered in young clusters, such as intra-cluster extinction and large uncertainties in BD models. Here we present the results of a deep photometric survey to study the MF of the old open cluster Praesepe (age 590+150-120 Myr and distance 190+6.0-5.8 pc), down to a 5σ detection limit at i˜25.6 mag (˜40 MJup). We identify 62 cluster member candidates, of which 40 are substellar, from comparison with predictions from a dusty atmosphere model. The MF rises from the substellar boundary until ˜60 MJup and then declines. This is quite different from the form inferred for other open clusters older than 50 Myr, but seems to be similar to those found in very young open cluster, whose MFs peak at ˜10 MJup. Either Praesepe really does have a different MF from other clusters or they had similar initial MFs but have differed in their dynamical evolution. We further have identified six foreground T dwarf candidates towards Praesepe, which require follow-up spectroscopy to confirm their nature.