It is just as difficult to know whether Peter really was a spokes man for the intimate companions of Jesus during the Lord's ministry or whether the instances of such spokesmanship in the Gospels are not merely "the reflection of his later role as the spokes man for the twelve in the Jerusalem church."
9 As for the apostle's later life, while it is "most prob able" in the opinion of the task force that Simon Peter went to Rome late in his career and was martyred there, "the same cannot be said about the question of whether he served as local 'bishop' of the Roman community and whether he appointed his successors in the Roman bishopric."
10
The now classic collaborative effort (Protestant / Catholic) concerning the New Testament’s witness to Peter’s “primacy” is that of R. E. Brown, K. P. Donfried and John Reumann, eds.,
Peter in the New Testament (Minneapolis, 1973).
Good read