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With a sample of (225.2\pm2.8)*10^{6} J/psi events registered in the BESIIIdetector, J/psi->gamma pi^+ pi^- eta' is studied using two eta' decay modes:eta'->pi^+ pi^- eta and eta' -> gamma rho^0. The X(1835), which was previouslyobserved by BESII, is confirmed with a statistical significance that is largerthan 20\sigma. In addition, in the pi^+pi^-eta' invariant mass spectrum, theX(2120) and the X(2370), are observed with statistical significances largerthan 7.2\sigma and 6.4\sigma, respectively. For the X(1835), the angulardistribution of the radiative photon is consistent with expectations for apseudoscalar.

Confirmation of the X(1835) and observation of the resonances X(2120) and X(2370) in J/psi->gamma pi^+pi^-eta'