This study pertains to the Chi-Chi earthquake of 1999 (a Richter magnitude (ML) of 7.3), the Meishan earthquake of 1906 (a Richter magnitude (ML) of 7.1) and the Hualien earthquakes of 1951 (a Richter magnitude (ML) of 7.3), which were triggered by the Chelungpu, Meishan and Milun faults. Two back-propagation neural networks (BPNNs)—(1) an embedded earthquake Richter magnitude (ML) prediction BPNN model and (2) an active probability BPNN model—are used to predict recurrence times over 500 years. Recurrence times for a 500-year period have been studied previously. This study examines the three earthquakes again and compares the results with those for previous studies. This process does not use any probability model with exceedance probability. The Chelungpu fault and the Tamaopu-Shuangtung fault are shown to more strongly couple. This viewpoint agrees with previous studies, which suggests that the Chi-Chi earthquake was caused by the Chelungpu faults in 1999. Its recurrence time with a Richter magnitude (ML) of more than 7 is 210 years after the Chi-Chi earthquake, and the highest probability is more than 60%. The Meishan earthquake is confirmed to have been caused by the Meishan fault in 1906. There is a high probability of more than 60% of another Meishan earthquake with a Richter magnitude (ML) of more than 7 in 170 years. There is a high probability of more than 60% for the occurrence of an earthquake with a Richter magnitude (ML) of more than 7 in Hualien due to the Milun faults. The results for both BNNN models are more realistic than those of previous studies because only the earthquake catalog is used, so that the cost of study is reduced.