The unproven assumption that the Gutenberg–Richter (GR) relationship can be extrapolated to estimate the return time, (1/probability of occurrence), of major and large earthquakes has been shown to be incorrect along 196 faults, so far. Here, two more examples of great, well‐known faults that do not produce enough earthquakes to fulfill the hypothesis are analyzed. The 300 km section of the San Andreas fault, California, United States, that ruptured in 1906 in the M 8 San Francisco earthquake, produced 200 earthquakes with in the last 52 yr, when about 250,000 such events are expected according to the hypothesis. Along a 250 km section that broke in an M 7.9 earthquake in 1717 along the Alpine fault, New Zealand, the number of reported earthquakes during the last 34 yr was 100, when about 6000 would be expected, based on the hypothesis. Extrapolating the GR relationships for these two fault segments, one estimates of mainshocks of M 8 to be about 10,000 and 100,000 for the 1717 and 1906 ruptures, respectively. Regardless of choice of analysis parameters, this is by factors of 10–400 larger than estimates based on paleogeology, tectonics, and geodesy. In addition, second catalogs for each case yield estimates of probabilities for M 8 earthquakes along the 1717 and 1906 rupture segments that differ by factors of about 2 and 80 (between 5000 and 98,000 yr) from the first respective catalogs. It follows that the probability of large earthquakes cannot be estimated correctly based on local seismicity rates along major faults.