Central exclusive diffractive production (CEDP) of proton–anti-proton pairs is calculated in the Regge-eikonal approach taking into account continuum and possible f_0(2100) resonance. We use the simple model with the “scalar” proton. Data from ISR and STAR are analysed and compared with theoretical descriptions. Some predictions for the LHC at 13 TeV are also presented. We briefly discuss possible nuances, problems and prospects for investigations of this process at present and future hadron colliders.