  We present the MBR (Minimum Bias Rockefeller) Monte Carlo simulation of
(anti)proton-proton interactions and its implementation in the PYTHIA8 event
generator. We discuss the total, elastic, and total-inelastic cross sections,
and three contributions from diffraction dissociation processes that contribute
to the latter: single diffraction, double diffraction, and central diffraction
or double-Pomeron exchange. The event generation follows a
renormalized-Regge-theory model, successfully tested using CDF data. Based on
the MBR-enhanced PYTHIA8 simulation, we present cross-section predictions for
the LHC and beyond, up to collision energies of 50 TeV.
