An estimate of the flux of prompt atmospheric neutrinos produced in decays of charmed particles is obtained. Cross sections of the production of charmed particles (D, Λ c ) in pA and πA collisions are calculated in the quark-gluon string model (QGSM) for the energy range 1 TeV – 100 PeV. New data on the cross sections of charmed meson production at high energies, obtained in experiments at the Large Hadron Collider, make it possible to refine the values of the free parameters of the QGSM and obtain a preliminary estimate of the prompt atmospheric neutrino flux. A comparison is made with the results of other neutrino flux calculations carried out for other charm production models – the dipole model and SIBYLL 2.3rc1.