  The Padoan and Nordlund model of the stellar initial mass function (IMF) is
derived from low order statistics of supersonic turbulence, neglecting gravity
(e.g. gravitational fragmentation, accretion and merging). In this work the
predictions of that model are tested using the largest numerical experiments of
supersonic hydrodynamic (HD) and magneto-hydrodynamic (MHD) turbulence to date
(~1000^3 computational zones) and three different codes (Enzo, Zeus and the
Stagger Code). The model predicts a power law distribution for large masses,
related to the turbulence energy power spectrum slope, and the shock jump
conditions. This power law mass distribution is confirmed by the numerical
experiments. The model also predicts a sharp difference between the HD and MHD
regimes, which is recovered in the experiments as well, implying that the
magnetic field, even below energy equipartition on the large scale, is a
crucial component of the process of turbulent fragmentation. These results
suggest that the stellar IMF of primordial stars may differ from that in later
epochs of star formation, due to differences in both gas temperature and
magnetic field strength. In particular, we find that the IMF of primordial
stars born in turbulent clouds may be narrowly peaked around a mass of order 10
solar masses, as long as the column density of such clouds is not much in
excess of 10^22 cm^-2.
