We revisit the estimate of the charm particle contribution to the atmospheric neutrino flux that is expected to dominate at high energies because long-lived high-energy pions and kaons interact in the atmosphere before decaying into neutrinos. We focus on the production of forward charm particles which carry a large fraction of the momentum of the incident proton. In the case of strange particles, such a component is familiar from the abundant production of K+Λ pairs. These forward charm particles can dominate the high-energy atmospheric neutrino flux in underground experiments. Modern collider experiments have no coverage in the very large rapidity region where charm forward pair production dominates. Using archival accelerator data as well as IceCube measurements of atmospheric electron and muon neutrino fluxes, we obtain an upper limit on forward D¯0Λc pair production and on the associated flux of high-energy atmospheric neutrinos. We conclude that the prompt flux may dominate the much-studied central component and represent a significant contribution to the TeV atmospheric neutrino flux. Importantly, it cannot accommodate the PeV flux of high-energy cosmic neutrinos, or the excess of events observed by IceCube in the 30-200 TeV energy range indicating either structure in the flux of cosmic accelerators, or a presence of more than one component in the cosmic flux observed.