Paul and Peter in Rome
It is thought that St. Paul spent two years in Rome, the capital of the Roman Empire.
St. Peter also came to Rome. However, as Luke did not mention Peter in Rome in Acts, Peter must have come to Rome after Paul. But, as Luke, who followed Paul to Rome, probably wrote the Gospel and Acts in Rome taking a year or so, Peter came to Rome one year after Paul's arrival at Rome.
But why did not Luke rewrite or modify Acts to add Peter's arrival at Rome? It is because Luke must have become busy in preaching with Peter on streets, synagogues, etc. of Rome or Luke had already handed over his Acts to someone. As Paul was in a state of a kind of house arrest, Paul probably could not openly go out and preach the Gospel. So, he must have checked the Gospel.
Especially as the Gospel according to Luke was a translation from the source document Paul must have, Paul must have carefully checked it. And, furthermore, Mark came to Rome accompanying Peter, and Paul must have asked Mark also to translate the source document of the mission of Christ Jesus. However, as Mark had written some words of Peter in their journey to Rome, Luke must have also modified his version of the Gospel according to information in Mark's writing. So, Paul must have been busy checking Mark's version of the Gospel and Luke's version of Gospel.
In the meantime, Peter must have been exhaustively preaching the Gospel in Rome till Nero executed both Peter and Paul. Therefore, it was just for one year that Peter preached on Christ Jesus to Roman citizens. But his preaching must have been so moving and impressive to the citizens of Rome, so that Peter acquired many believers. Therefore, Peter was regarded as the First Pope even today.
Anyway, if Peter had not come to Rome, he could not have been regarded as the first Pope especially by Christians in Rome in subsequent years. But, it was just one year's activities that allowed Peter to be honored as the First Pope.
One question is that whether Peter used the Gospels according to Luke and Mark in his preaching in Rome? These Gospels might have been still checked by Paul under house arrest. However, if Peter had used these Gospels in his mission, these Gospels should have become naturally more authentic.
In either case, it is also natural that the Gospel according to Luke, a follower of Paul, and the Gospel according to Mark, a follower of Peter, became canonical. And, if Paul had also asked Mathew to translate the original Hebrew/Aramaic source into a Greek Gospel, the Gospel according Mathew is also canonical.
Put simply, it is thought these Gospels must have been written based on the same source document, which Paul must have kept since he had obtained it probably in Qumran, in the same period of time such as during Paul's house arrest in Rome till his death.
The church in Rome was already flourishing when Paul wrote his Epistle to the Romans about AD 57, he greets some fifty people in Rome by name, but not Peter whom he knew. There is also no mention of Peter in Rome later during Paul's two-year stay there in Acts 28, about AD 60-62. Some Church historians consistently consider Peter and Paul to have been martyred under the reign of Nero, around AD 65.
In a strong tradition of the Early Church, Peter is said to have founded the Church in Rome with Paul, served as its bishop, authored two epistles, and then met martyrdom there along with Paul. Christians of different theological backgrounds are in disagreement as to the exact significance of Peter's ministry. For instance:
Roman Catholics view Peter as the first pope. The Roman Catholic Church asserts that Peter's ministry, conferred upon him by Jesus of Nazareth in the gospels, lays down the theological foundation for the pope's exercise of pastoral authority over the Church.
Eastern Orthodox also believe that Peter's ministry points to an underlying theology wherein a special primacy ought to be granted to Peter's successors above other Church leaders but see this as merely a "primacy of honor", rather than the right to exercise pastoral authority.
Protestant denominations assert that Peter's apostolic work in Rome does not imply a connection between him and the papacy.
Similarly, historians of various backgrounds also offer differing interpretations of the Apostle's presence in Rome.
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Luk 2:10 And the angel said unto them, Fear not: for, behold, I bring you good tidings of great joy, which shall be to all people.
Luk 2:11 For unto you is born this day in the city of David a Saviour, which is Christ the Lord.