Romans 16:23
Gaius mine host, and of the whole church, saluteth you. Erastus the chamberlain of the city saluteth you, and Quartus a brother. Gaius mine host, and of the whole church, saluteth you. Erastus the chamberlain of the city saluteth you, and Quartus a brother.
Romans was written in A.D. 58 from Corinth and sent by Phebe from Cenchrea to the Christian church at Rome, then the metropolis of the world, whose members were former heathen who had embraced the gospel and Jews who believed in Jesus as the Messiah while still retaining many prejudices. The church at Rome was founded by Jews and proselytes from Jerusalem converted on the Day of Pentecost, with others added afterward, and the large number of salutations in Romans 16 reflects that origin and growth. The verse records greetings from Gaius, Paul's host and host of the whole church, and from Erastus the city treasurer or chamberlain, and Quartus a brother and fellow believer.
The names show Paul knew many people in the Roman church, including fellow workers and converts connected with his ministry, many of whom he had met on his travels. The many women named in the chapter's greetings show that women had important roles among the people greeted. Peter's name is absent from the long greeting of Roman believers by name, which shows Peter was not in Rome when Romans was written.
Paul would certainly not have omitted Peter if Peter had been there, especially after spending fifteen days with him in Jerusalem. The absence shows Peter was not Bishop of Rome and was not the chief person in the Roman church, settling that neither the church of Christ nor the church of Rome was founded upon Peter. If Peter was ever in Rome, it was after Romans was written and long after the church there was established and flourishing.