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Prompt fission neutrons following the thermal and 0.5 MeV neutron-induced fission reaction of 239 Pu are calculated using a Monte Carlo approach to the evaporation of the excited fission fragments. Exclusive data such as the multiplicity distribution P (ν), the average multiplicity as a function of fragment mass ν(A), and many others are inferred in addition to the most used average prompt fission neutron spectrum χ (E in , E out), as well as average neutron multiplicity ν. Experimental information on these more exclusive data help constrain the Monte Carlo model parameters. The calculated average total neutron multiplicity is ν c = 2.871 in very close agreement with the evaluated value ν e = 2.8725 present in the ENDF/B-VII.0 library. The neutron multiplicity distribution P (ν) is in very good agreement with the evaluation by Holden and Zucker. The calculated average spectrum differs in shape from the ENDF/B-VII.0 spectrum, evaluated with the Madland-Nix model. In particular, we predict more neutrons in the low-energy tail of the spectrum (below about 300 keV) than the Madland-Nix calculations, casting some doubts on how much scission neutrons contribute to the shape of the low-energy tail of the spectrum. The spectrum high-energy tail is very sensitive to the total kinetic energy distribution of the fragments as well as to the total excitation energy sharing at scission. Present experimental uncertainties on measured spectra above 6 MeV are too large to distinguish between various theoretical hypotheses. Finally, comparisons of the Monte Carlo results with experimental data on ν(A) indicate that more neutrons are emitted from the light fragments than the heavy ones, in agreement with previous works.