The occurrence of 5 Mw ≥ 8.5 earthquakes since 2004 has created a debate over whether or not we are in a global cluster of large earthquakes, temporarily raising risks above long-term levels. I use three classes of statistical tests to determine if the record of M ≥ 7 earthquakes since 1900 can reject a null hypothesis of independent random events with a constant rate plus localized aftershock sequences. The data cannot reject this null hypothesis. Thus, the temporal distribution of large global earthquakes is well-described by a random process, plus localized aftershocks, and apparent clustering is due to random variability. Therefore the risk of future events has not increased, except within ongoing aftershock sequences, and should be estimated from the longest possible record of events.