We report on the correlation between the number of >500 MeV protons (Ng) deduced from the Fermi/LAT >100 MeV sustained gamma-ray emission (SGRE) and the number of protons at 1 au (NSEP) estimated from PAMELA mission’s solar energetic particle (SEP) measurements. The correlation is highly significant with a correlation coefficient of 0.77 and hence supports the shock origin of >300 MeV protons that interact with the solar chromosphere and resulting in pion decay observed as SGRE. The lack of correlation previously reported has been shown to be due to (i) a systematic underestimate of Ng in events originating close to the limb owing to the spatially-extended nature of SGRE, and (ii) a systematic underestimate of NSEP in events originating at higher latitudes as a consequence of poor latitudinal connectivity. Correcting for these to effects, we find that the regression line is close to the Ng = NSEP line. The close correlation found between NSEP and Ng indicating their common origin (the CME-driven shock) is consistent with other significant correlations: (i) between the SGRE duration and the duration of the associated interplanetary type II radio burst, and (ii) between the SGRE fluence and CME speed.