Context. Determination of the mass functions of open clusters of different ages allows us to infer the efficiency with which brown dwarfs are evaporated from clusters to populate the field. Aims: In this paper we present the results of a photometric survey to identify low mass and brown dwarf members of the old open cluster Praesepe (age 590+150-120 Myr, distance 190+6.0-5.8 pc) from which we estimate its mass function and compare this with that of other clusters. Methods: We performed an optical (I_c-band) and near-infrared (J and K_s-band) photometric survey of Praesepe covering 3.1 deg2. With 5σ detection limits of I_c=23.4 and J = 20.0, our survey is predicted to be sensitive to objects with masses from 0.6 to 0.05 M_&sun;. Results: We photometrically identify 123 cluster member candidates based on dust-free atmospheric models and 27 candidates based on dusty atmospheric models. The mass function rises from 0.6 M_&sun; down to 0.1 M_&sun; (a power law fit of the mass function gives α = 1.8 ± 0.1; ξ(M) ∝ M-α ), and then turns over at ~0.1 M_&sun;. This rise agrees with the mass function inferred by previous studies, including a survey based on proper motion and photometry. In contrast, the mass function differs significantly from that measured for the Hyades, an open cluster with a similar age (τ ˜ 600 Myr). Possible reasons are that the clusters did not have the same initial mass function, or that dynamical evolution (e.g. evaporation of low mass members) has proceeded differently in the two clusters. Although different binary fractions could cause the observed (i.e. system) mass functions to differ, there is no evidence for differing binary fractions from measurements published in the literature. Of our cluster candidates, six have masses predicted to be equal to or below the stellar/substellar boundary at 0.072 M_&sun;. Based in part on observations carried out at ESO/La Silla, Chile under proposal number 078.A-9055(A).Full Table 3 is only available in electronic form at http://www.aanda.org