Solar proton events (>10 Mev) with flux higher than 10,000 particle/cm2-s-sr (pfu) and the associated coronal mass ejection CME events are listed in the NOAA online catalog. There were five events between 1997 and June 2003 with proton flux from 12,900 to 31,700 pfu and they produced strong geomagnetic storms. The analysis shows that the three highest proton flux events correlate with (r=0.96) either the speed or (r=0.97) energy of the CME. The small intercept suggests a speed threshold indicative of solar wind contribution. The two lowest flux events do not so correlate but exhibit prolonged (4-day) decay behavior for the 100 Mev protons (GOES data) when compared to the (2-day) decay typical of the three higher flux events. The interpretation of shorter diffusion mean free path in the interplanetary transport equation for the lower flux events is consistent with the conjecture that the prolonged temporal decay is due to the extra scattering when the associated CME collides with the preceding halo CME. The Ulysses satellite uses full plasma and magnetic data to identify CME events and it also detected two CME events subsequent to the GOES flux signature of these two lower flux events. The subsequent time delay and Ulysses location in the heliosphere is consistent with the diffusion interpretation. The waiting time distribution of high speed and halo CME events could be used to enhance the prediction of the geoeffective high flux solar proton event.