We present the results of ROSAT PSPC observations of the Praesepe cluster. 68 Praesepe candidates have been detected, above a threshold of ≃2x1028erg/s, in the ∼4x4deg area of the cluster covered by the observations. 56 out of the 68 detected objects are cataloged as high probability Praesepe members. Praesepe members of all spectral types have been detected with X-ray luminosities ranging from the sensitivity limit to approximately 1030erg/s in the ROSAT broad band. The highest X-ray luminosity has been measured for a very short period W UMa type SB2 binary. 2 out of the 4 Praesepe late-type giants have also been detected. X-ray luminosity distribution functions have been derived for late-type stars in the sample, taking into account both detections and upper limits. The main and most surprising finding are the low detection rates derived for Praesepe low mass dwarfs. We detected about 30% of the F and G stars, and the detection rate among K and M dwarfs is even lower. Correspondingly, the luminosity distribution functions for stars in selected color intervals are dominated by the contribution of upper limits, with the medians below the sensitivity threshold. The comparison with the Hyades all-sky survey results shows an evident discrepancy between the average X-ray properties of late-type dwarfs in the two apparently coeval clusters; such a discrepancy must be an intrinsic one, since the observations are characterized by similar sensitivities.
open clusters and associations: individual: Praesepe - stars: coronae - X-ray: stars