Peter and Paul were the Apostles who graced the Church of Rome, were martyred and buried there and thereby gave that Church a prestige enjoyed by no other. As to the role of Peter among the apostles, it was like Paul, that of a missionary, not an administrator. No questioning his prominent place among them, as can be seen in the Gospels and in Acts. It was he was, after all, was assigned the role of proclaiming the New Covenant to the assemple people of Israel on the day of Pentecost, when 3,000 were added in one day to the Church. It is he who is the central ":character" in the first part of Acts, until Paul is "spotlighted." The very way that Luke has him exit the" stage" has led to the suggestion that Luke intended to write more about him, so that if the good doctor has picked up his pen again, we might have learned more about Peter just as we might have learned more about Paul.
There is no doubt that by the middle of the 2nd century that a "bishop" of Rome existed, an offical whose authority was based on his connection with the "tradition" of Peter and Paul. Nor much doubt that it was his association with Peter that removed all suspicious of Paul, whose doctrines were sometimes appropriated by heretics. Irenaeus in fact gives us the "lineage" of the "popes" of Rome, although --it may be--that the authority of the Church of Rome was at least originally informal and even collective. Protestant hostility to the veneration of relics predisposes them to dismiss out of hand the devotion that early on drew pilgrims to Rome to pray at the tombs of the apostles. But it happened. The centrality of Rome in the Empire was paralleled by the centrality of Rome in the place. The destruction of Jerusalem in 70 made this almost inevitable, even though the churches in the East always far exceeded number those in the West. The strong monarchical authority of the papacy was an historical accident, or an act of providence. The spiritual authority upon which it based was owing to Peter. whose authority was of divine origin.
Peter was never in Rome.....and in fact, was told to stay out of there! [Matthew 10:5-6] These twelve Jesus sent forth, and commanded them, saying, Go not into the way of the Gentiles, and into any city of the Samaritans enter ye not: But go rather to the lost sheep of the house of Israel.
Like the article said.....that's why The Lord chose Paul.
7On the contrary, they saw that I had been entrusted with the task of preaching the gospel to the Gentiles, just as Peter had been to the Jews. 8For God, who was at work in the ministry of Peter as an apostle to the Jews, was also at work in my ministry as an apostle to the Gentiles. 9James, Peter and John, those reputed to be pillars, gave me and Barnabas the right hand of fellowship when they recognized the grace given to me. They agreed that we should go to the Gentiles, and they to the Jews. 10All they asked was that we should continue to remember the poor, the very thing I was eager to do.
--Galatians 2:7-10