The physics of earthquake triggering together with simple assumptions of self-similarity imply the existence of a minimum magnitude m0 below which earthquakes do not trigger other earthquakes. Noting that the magnitude md of completeness of a seismic catalog is not, in general, the same as the magnitude m0 of the smallest triggering earthquake, we compare observed aftershock sequence parameters with the predictions made by the epidemic-type aftershock sequence model to constrain the value of m0. In particular, we use quantitative fits to observed aftershock sequences from three previous studies, as well as Båth's law, to obtain four estimates of m0. We show that the branching ratio n (average number of triggered earthquakes per earthquake, also equal to the fraction of aftershocks in a seismic catalog) is the key parameter controlling the estimate of the minimum triggering magnitude m0. Conversely, physical upper bounds for m0 estimated from rate and state friction indicate that at the very least, 55% of all earthquakes are aftershocks.