Schaff, Philip. History of the Christian Church (The Complete Eight Volumes in One). Amazon Kindle Edition, 2014.
Volume 2, Ante-Nicene Christianity A.D. 100-325, “Chapter 4. Organization and Discipline of the Church” Loc. 13792-14769 (part 7).
§51. Chronology of the Popes.
Schaff lists a chronology of the bishops of Rome. He notes that these chronologies come from varied sources and have differences. He divides the actual chronologies into those from eastern sources and western sources (Schaff 2014, Loc.14296). In addition to literary sources, he notes inscriptions discovered since 1850, but without dates (Schaff 2014, Loc.14303). The sources are not in complete agreement. Schaff goes on to note some of the more important editions and scholarly works used to establish the chronology. Notably, in the first century, some include Peter, while some separate him as an apostle, not a bishop (Schaff 2014, Loc.14324). Though there is some doubt about the individuals and dates, Schaff observes the records at Rome are more completee and clear than those in other centers of Christianity (Schaff 2014, Loc.14333).
§52. List of the Roman Bishops and Roman Emperors during the First Three Centuries.
Schaff continues with his interpretation of the bishops and emperors and their dates (Schaff 2014, Loc.14337-14365). On average, during this period, popes served for about seven years.