The Church Fathers on: Primacy of Peter and Peter in Rome

What did the earliest Christians believe about Peter's Primacy and whether his "See" was in Rome?  Why not let them speak for themselves?  Here is just a tidbit for starters:

"The blessed Peter, the chosen, the preeminent, the first of the disciples, for whom alone and himself the Savior paid tribute [Mt 17:27], quickly seized and comprehended the saying...” (Clement of Alexandria, Who is the rich man that shall be saved? 21, AD 200)

Quoting Mt 16:18-19, Tertulian rebukes, “What kind of man are you, subverting and changing what was the clear intent of the Lord when he himself conferred this upon Peter? Upon YOU, he says, I will build my Church; and I will give to YOU the keys.” (emphasis in original, Tertullian, Modesty 21, AD 220)

Cyprian of Carthage explains likewise as Tertullian and Clement, and emphasizes, “Indeed, the others were also what Peter was [apostles], but a primacy is given to Peter, by which it is made clear that there is one Church and one chair...” (Cyprian, Unity of the Catholic Church 4; first edition, Treatise 1:4, AD 251)

Ignatius of Antioch, writing to the Romans, gives evidence that Peter was in Rome: “I do not, as Peter and Paul, issue commandments unto you. They were apostles; I am but a condemned man: They were free, while I am, even now, a servant.” (Ignatius, Letter to the Romans 4, AD 110)

“You [Pope Soter] have thus by such an admonition bound together the planting of Peter and Paul at Rome and Corinth. For both of them planted and taught us in Corinth. And they taught together in Italy, and suffered martyrdom at the same time.” (Dionysius of Corinth, Letter to Pope Soter, AD 170...in Eusebius' “Church History” 2:25:8)

“Matthew also issued among the Hebrews a written Gospel in their own language, while Peter and Paul were evangelizing in Rome and laying the foundation of the Church.” (Irenaeus, Against Heresies, 3:1:1, AD 189)

“Since moreover, you are close upon Italy, you have Rome, from which there comes even into our own hands the very authority (of the apostles themselves) [sic]. How happy is its church, on which apostles poured forth all their doctrine along with their blood! Where Peter endures a passion like his Lord's! Where Paul wins his crown in a death like John's! Where the apostles John was first plunged, unhurt, into boiling oil, and thence remitted to his island exile!” (Tertullian, Prescription Against Heretics 36, AD 200)

“Victor...was the thirteenth bishop of Rome from Peter.” (Eusabius, Church History 5:28:3, AD 312)

There are a dozen more or so putting Peter in Rome. I don't claim these are proof texts and explicit evidences...but they are a clear insight into the understanding of the earliest of Christians about Papal Primacy and Peter being in Rome.