Measurements are taken of the mantle magnitudeM _m , developed and introduced in previous papers, in the case of the 1960 Chilean and 1964 Alaskan earthquakes, by far the largest events ever recorded instrumentally. We show that theM _m algorithm recovers the seismic moment of these gigantic earthquakes with an accuracy (typically 0.2 to 0.3 units of magnitude, or a factor of 1.5 to 2 on the seismic moment) comparable to that achieved on modern, digital, datasets. In particular, this study proves that the mantle magnitudeM _m does not saturate for large events, as do standard magnitude scales, but rather keeps growing with seismic moment, even for the very largest earthquakes. We further prove that the algorithm can be applied in unfavorable experimental conditions, such as instruments with poor response at mantle periods, seismograms clipped due to limited recording dynamics, or even on microbarograph records of air coupled Rayleigh waves. In addition, we show that it is feasible to use acoustic-gravity air waves generated by those very largest earthquakes, to obtain an estimate of the seismic moment of the event along the general philosophy of the magnitude concept: a single-station measurement ignoring the details of the earthquake's focal mechanism and exact depth.