Primary proton spectrum in the energy range $5-10^3$ TeV from the sea   level muon spectrum
  Primary proton spectrum in the energy range $5-10^3$ TeV is reconstructed from the sea level muon spectrum with the use of QGSJET01 and SYBILL2.1 interaction models. Heavier nuclei are taken in accordance with the direct measurements data, 100% uncertainty in helium flux is accounted for. The obtained proton intensity strongly contradicts to the available data of balloon experiments, exceeding them at the least by 100% for QGSJET01. This discrepancy is due to the combined effect of primary nucleon flux underestimation in the direct measurements and incorrect description of extensive air shower development. In the latter case it is required earlier shower development and harder spectra of secondary pions and kaons in comparison with QGSJET01. This conclusion is in agreement with the obtained by the KASCADE group on the basis of events rate study. 
A. A. Lagutin, A. G. Tyumentsev, A. V. Yushkov