Context : Studies of the mass function ( MF ) of open clusters of different ages allow us to probe the efficiency with which brown dwarfs evaporate from clusters to populate the field . Surveys of older clusters ( age \gtrsim 100 Myr ) are not affected so severely by several problems encountered in young clusters , such as intra-cluster extinction and large uncertainties in brown dwarf models . Aims : We present the results of a deep photometric survey to study the MF of the central region of the old open cluster Praesepe ( age 590 ^ { +150 } _ { -120 } Myr , distance 190 ^ { +6.0 } _ { -5.8 } pc ) , down to the substellar regime . Methods : We performed an optical ( riz and Y -band ) photometric survey of Praesepe using the Large Binocular Telescope Camera covering an area of 0.59 deg ^ { 2 } in the cluster centre from i \sim 19.0 mag ( \sim 100 M _ { Jup } ) down to a 5 \sigma detection limit at i \sim 25.6 mag ( \sim 40 M _ { Jup } ) . The survey is approximately 95 % complete at i = 23.8 mag and z = 22.0 mag ( \sim 55 M _ { Jup } ) . Results : We identify 59 cluster member candidates , of which 37 are substellar , by comparing with the predictions of a dusty atmosphere model . The MF of those candidates rises from the substellar boundary until \sim 67 M _ { Jup } 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 clusters , the MFs of which peak at \sim 10 M _ { Jup } . Either Praesepe really does have a different MF from other clusters or they had similar initial MFs but a different dynamical evolution . Since most of the candidates are faint , we lack astrometric or spectroscopic follow-ups to test their memberships . However , the contaminations by field dwarfs , galaxies , or giants are found to have little effect on the shape of MF and therefore the MF of ‘ real ’ cluster members should have similar characteristics . Conclusions :