We consider unfavoured light quark/antiquark to D meson fragmentation. We discuss nonperturbative effects for small transverse momenta. The asymmetry for D+ and D- production measured by the LHCb collaboration provides natural constraints on the parton (quark/antiquark) fragmentation functions. We find that already a fraction of $q/\overline q \to D$ fragmentation probability is sufficient to account for the measured asymmetry. Large D-meson production asymmetries are found for large xF which is related to dominance of light quark/antiquark $q/\overline q \to D$ fragmentation over the standard c → D fragmentation. As a consequence, prompt atmospheric neutrino flux at high neutrino energies can be much larger than for the conventional c → D fragmentation. The latter can constitute a sizeable background for the cosmic neutrinos claimed to be observed recently by the IceCube Observatory.