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The energy spectrum of cosmic rays above 2.5 x 1018 eV, derived from 20 000 events recorded at the Pierre Auger Observatory, is described. The spectral index γ of the particle flux, J/ E- γ , at energies between 4 x 1018 eV and 4 x 1019 eV is 2.69 ± 0.02(stat) ± 0.06(syst), steepening to 4.2 ± 0.4(stat) ± 0.06(syst) at higher energies. The hypothesis of a single power law is rejected with a significance greater than 6 standard deviations. The data are consistent with the prediction by Greisen and by Zatsepin and Kuz’min.