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For the past 30 years, the M8 medium-term earthquake prediction algorithm has been applied globally every six months in real time for identifying the areas where the world’s strongest earthquakes are most likely to occur. As of now, the statistics of the outcomes observed in the Global Test with a confidence exceeding 99% indicates fairly high efficiency of the forecasts based on the M8 algorithm and those based on its combination with the MSc algorithm which more accurately localizes the focal zone of the expected earthquake. Thus, the null hypothesis of random occurrence in seismically active areas is rejected with seismologically certainty at least for the world’s strongest earthquakes in the magnitude ranges 8.0+ and 7.5+. The results of this experimental testing indirectly confirm the predictability of the strong earthquakes and the existence of both the common dynamic characteristics and diverse behavior during phase transitions in a complex hierarchical nonlinear fault-and-block system in the Earth’s lithosphere.