My concern is as follows. Irenaeus says that all the churches worked together from the very beginning. There is a supernatural quality to this testimony. It implies that the normal relationship among humans was overcome by divine intervention. Whatever is original from 1 Clement, the idea that the Roman Church was responding to a request from the Corinthian church to admonish them undoubtedly was a revision. A revision of what no one knows. But Justin isn't the next logical step.
The next logical step is Hegesippus. The myth or story of Hegesippus is intimately connected to this relationship between Rome and Corinth. It goes back to Lawlor's idea that Epiphanius has Hegesippus in his hand when citing the following words in italics:
I heard at some time of a Marcellina who was deceived by them, who corrupted many people in the time of Anicetus, Bishop of Rome, the
successor of Pius and the bishops before him. For the bishops at Rome were, first, Peter and Paul, the apostles themselves and also bishops—then Linus, then Cletus, then Clement, a contemporary of Peter and Paul whom Paul mentions in the Epistle to the Romans. And no one need wonder why others before him succeeded the apostles in the episcopate, even though he was contemporary with Peter and Paul—for he too is the apostles’ contemporary. I am not quite clear as to whether he received the episcopal appointment from Peter while they were still alive, and he declined and would not exercise the office—for in one of his Epistles he says, giving this counsel to someone, “I withdraw, I depart, let the people of God be tranquil,”29 (I have found this in certain historical works)—or whether he was appointed by the bishop Cletus after the apostles’ death.
But even so, others could have been made bishop while the apostles, I mean Peter and Paul, were still alive, since they often journeyed abroad
for the proclamation of Christ, but Rome could not be without a bishop. (6) Paul even reached Spain, and Peter often visited Pontus and Bithynia.
But after Clement had been appointed and declined, if this is what happened—I suspect this but cannot say it for certain—he could have been
compelled to hold the episcopate in his turn, after the deaths of Linus and Cletus who were bishops for twelve years each after the death of Saints
Peter and Paul in the twelfth year of Nero.)
In any case, the succession of the bishops at Rome runs in this order: Peter and Paul, Linus and Cletus, Clement, Evaristus, Alexander, Xystus,
Telesphorus, Hyginus, Pius, and Anicetus, whom I mentioned above, on the list. And no one need be surprised at my listing each of the items so exactly; precise information is always given in this way. (8) In Anicetus’ time then, as I said, the Marcellina I have spoken of appeared at Rome spewing forth the corruption of Carpocrates’ teaching, and corrupted and destroyed many there. And that made a beginning of the so-called Gnostics.
They have images painted with colors—some, moreover, have images made of gold, silver and other material—which they say are portraits of Jesus, and made by Pontius Pilate! That is, the portraits of the actual Jesus while he was dwelling among men! (10) They possess images like these in secret, and of certain philosophers besides—Pythagoras, Plato, Aristotle, and the rest—and they also place other portraits of Jesus with
these philosophers. And after setting them up they worship them and celebrate heathen mysteries. For once they have erected these images, they go on to follow the customs of the heathen. But what are < the > customs of the heathen but sacrifices and the rest? (11) They say that salvation is of the soul only, and not of bodies.
The way that I read the material from Hegesippus is that Peter and Paul represent one time period and two separate churches, Linus and Cletus another pairing and then Clement begins a single line of Roman bishops that extends into all that follows. The reason I think this is that Epiphanius appears to be baffled at some piece of evidence which suggests that Peter did not immediately install him on the throne. The implication seems to be that Clement was traveling around before being installed by Peter. This necessarily means that Clement, though from the third generation of Church leadership was installed while Peter was alive or between 60 - 66 CE.
Notice also that my idea of two pairs:
Πέτρος καὶ Παῦλος, Λίνος καὶ Κλῆτος,
and then a single line:
Κλήμης Εὐάρεστος Ἀλέξανδρος
allows makes 'Xystos' the 'sixth':
1. Πέτρος καὶ Παῦλος
2. Λίνος καὶ Κλῆτος
3. Κλήμης (= 60 CE)
4. Εὐάρεστος
5. Ἀλέξανδρος
6. Ξύστος
As many know 'Xystos' is often rendered 'Sextus' because of an identification of him as 'sixth' from the apostles. The understanding seems to have been introduced by Irenaeus:
The blessed Apostles, then, having founded and built up the Church, committed to Linus the administration of its episcopate. . . . Anencletus succeeds him, from whom in the third place from the Apostles Clemens inherits the episcopate. . . . He is succeeded by Evaristus; Evaristus by Alexander, who is followed by Xystus sixth from the Apostles. Then Telesphorus, who was gloriously martyred; next Hyginus; then Pius; after whom Anicetus
Irenaeus's list necessarily assumes that Peter and Paul weren't counted as the first bishops of Rome:
1. Linus
2. Anacletus
3. Clement
4. Evaristus
5. Alexander
6. Xystus the sixth
Yet it is obvious that Irenaeus has 'rejigged' the Hegesippian list. First of all he has removed the separateness of the Pauline line (i.e. the double pairing at the beginning) making Linus the Petrine bishop first and then Anacletus second. There are many other variants from Tertullian, Cyprian among others. But what they are trying to get away from is Gaius of Rome's observation of separate shrines for Peter and Paul thus emphasizing the existence of separate communities in the early days.
It should also be noted that if Clement was installed c 60 CE then that means that Hegesippus's own composition is much earlier than Irenaeus has it. An underlying connection with the chronology attributed to 'Joseph the Jew' in Clement viz. 147 CE is undoubtedly true. To this end, 'Joseph' goes to Rome under Anicetus sees Marcellina (in other traditions 'Marcion') which necessarily means earlier in the second century.
1. Πέτρος καὶ Παῦλος
2. Λίνος καὶ Κλῆτος
3. Κλήμης (= 60 CE)
4. Εὐάρεστος
5. Ἀλέξανδρος
6. Ξύστος
7. Τελέσφορος
8. Ὑγῖνος
9. Πίος
10. Ἀνίκητος
This seems to jibe with the tradition that Papias knew and reported on Marcion.
As an aside there is a tradition that Irenaeus established the Galatians-first canon supposedly transferred to Ephrem the Syrian via Palut c. 200 CE. We might see Irenaeus's taking Peter and Paul to be 'universal bishops' not attached to Rome as related to this effort. Peter was theoretically also the bishop of Antioch according to Syrian tradition. Only the Roman tradition would have emphasized 'Peter and Paul' as proper Roman bishops. He might not have liked the implication of separate churches at the beginning. The Marcionites might have had Paul, Cletus and then a list of successors perhaps extending through Clement, who knows.
I will offer one more bit of conjecture. Let's suppose that 'Xystos' originally described Telephorus as 'sixth':
1. Πέτρος καὶ Παῦλος
2. Λίνος καὶ Κλῆτος
3. Κλήμης (= 60 CE)
4. Εὐάρεστος
5. Ἀλέξανδρος
6. Τελέσφορος
7. Ὑγῖνος
8. Πίος
9. Ἀνίκητος
Nine is a strange number. Could 'Pius' have originally been another misunderstanding of a Latin text? In other words an adjective. As such we would end up with an ogdoad:
1. Πέτρος καὶ Παῦλος
2. Λίνος καὶ Κλῆτος
3. Κλήμης (= 60 CE)
4. Εὐάρεστος
5. Ἀλέξανδρος
6. Τελέσφορος
7. Ὑγῖνος
8. Ἀνίκητος
At the very least we can see that there appears to be Hegesippus's list - possibly written 147 CE - reflecting on an original visit to Rome and then Irenaeus's extending this list down to his own times by means of editorial revision. The fact that Irenaeus identifies Valentinus and Marcion in association with Telephoros and Anicetos is one thing. But Hegesippus identified or his testimony implied that Marcellina was the 'first gnostic.' This is clear from Epiphanius's citation.