Fundamentally related to the UV divergence problem in Physics, conventional wisdom in seismology is that the smallest earthquakes, which are numerous and often go undetected, dominate the triggering of major earthquakes, making the prediction of the latter difficult if not inherently impossible. By developing a rigorous validation procedure, we show that, in fact, large earthquakes (above magnitude 6.3 in California) are preferentially triggered by large events. Because of the magnitude correlations intrinsic in the validated model, we further rationalize the existence of earthquake doublets. These findings have far-reaching implications for short-term and medium-term seismic risk assessment, as well as for the development of a deeper theory without UV cut-off that is locally self-similar.