We investigate the sequence of great earthquakes over the past century. To examine whether the earthquake record includes temporal clustering, we identify aftershocks and remove those from the record. We focus on the recurrence time, defined as the time between two consecutive earthquakes. We study the variance in the recurrence time and the maximal recurrence time. Using these quantities, we compare the earthquake record with sequences of random events, generated by numerical simulations, while systematically varying the minimal earthquake magnitude Mmin. Our analysis shows that the earthquake record is consistent with a random process for magnitude thresholds 7.0≤Mmin≤8.3, where the number of events is larger. Interestingly, the earthquake record deviates from a random process at magnitude threshold 8.4≤Mmin≤8.5, where the number of events is smaller; however, this deviation is not strong enough to conclude that great earthquakes are clustered. Overall, the findings are robust both qualitatively and quantitatively as statistics of extreme values and moment analysis yield remarkably similar results.