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The transverse momentum (pT) distribution of primary charged particles is measured in minimum bias (non-single-diffractive) p-Pb collisions at sNN−−−√=5.02 TeV with the ALICE detector at the LHC. The pT spectra measured near central rapidity in the range 0.5<pT<20 GeV/c exhibit a weak pseudorapidity dependence. The nuclear modification factor RpPb is consistent with unity for pT above 2 GeV/c. This measurement indicates that the strong suppression of hadron production at high pT observed in Pb-Pb collisions at the LHC is not due to an initial-state effect. The measurement is compared to theoretical calculations.