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The article describes a study of the multiple pion production through observation of gamma-rays produced by nuclear interactions at the target layer of the emulsion chambers exposed at Chacaltaya, Bolivia, 5200 m above sea level. The analysis was focused on 80 events with ΣEr>20 TeV, well above the detection threshold of the X-ray film spot scanning, ∼3 TeV. The distribution of gamma-rays is constructed on their energy, pt, and emission angle, and the comparison is made with the results from the simulation calculations based on FNAL hydrogen bubble chamber events and ISR minimum bias events. The cosmic-ray results are significantly out of the simple scaling extrapolation, showing higher rapidity density nr. and increasing pt. Recent p-p collider experiments gave the confirming results. From the plot of events in the diagram of nr. and 〈pt〉, the events are classified into two types; Mirim-jets (meaning small jets, nr= 2∼3, 〈pt〉∼140 MeV/c) and Açu-jets (large jets, nr = 6∼8, 〈pt〉∼220 MeV/c), with nearly equal frequency of production. Mirim-jets are those on the scaling extrapolation from the lower energy region of accelerators, while increasing rate of Açu-jets with energy is causing the scaling break. The analysis with the fire-ball model shows that the Mirim-jets are consistently interpreted as production and decay of a small fire-ball (a fire-ball quantum called H-quantum) with rest energy of 2∼3 GeV and decay temperature of about 130 MeV. While, the Açu-jets necessitate introduction of a heavy fire-ball (SH-quantum) with rest energy of 20∼30 GeV. The study of atmospheric interactions (A-jets) shows presence of events with still larger nr and higher pt, which are called Guaçu-jets. One C-jet is found to be a candidate of this type. The Guaçu-jets require presence of a huge fire-ball (UH-quantum) of rest energy 200∼300 GeV. Discussions are made on physical implication of the fire-ball model, particularly on those quanta of a fire-ball.