One word in one sentence decides whether the earliest list of the bishops of Rome was written in the second century or not, and the word is the one this project is named after. Eusebius quotes Hegesippus saying that when he came to Rome he remained there until Anicetus, whose deacon was Eleutherus. The manuscripts read diatriben, a stay. An old conjecture reads diadochen, a succession, and on that reading the sentence means he compiled a list of the Roman bishops down to Anicetus — which would make him the first person known to have done it, and would put a written Roman succession a generation earlier than Irenaeus. The conjecture is attractive and this project has every temptation to want it. The evidence does not support it. Diadoche is not otherwise used to mean a catalogue; and Eusebius, who pursues succession lists through five books and quotes Hegesippus more often than he quotes almost anyone, never reproduces such a list and never refers to one, giving Irenaeus' instead when he needs it. The stay is the better reading. What Hegesippus did do at Rome is not in dispute and is remarkable enough: he went from church to church asking what each of them taught, and reported that they all said the same thing.
Ecclesiastical History · HE 4.22.1-3