We present an analysis of the Lambda(1405) resonance produced in the reaction p+p->Sigma^{pm}+pi^{mp}+K+p at 3.5 GeV kinetic beam energy measured with HADES at GSI. The two charged decay channels Lambda(1405) -> Sigma^{pm}+pi^{mp} have been reconstructed for the first time in p+p collisions. The efficiency and acceptance-corrected spectral shapes show a peak position clearly below 1400 MeV/c^2. We find a total production cross section of sigma_{Lambda(1405)}=9.2 +- 0.9 +- 0.7 +3.3-1.0 mub. The analysis of its polar angle distribution suggests that the Lambda(1405) is produced isotropically in the p-p center of mass system.
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