From Anglican scholar J.N.D. Kelly The Oxford Dictionary of Popes (1986) under Peter, St, Apostle (page 5-6)
"The papacy, through successive popes and councils, has always traced its origins and title-deeds to the unique commission reported to have been given by Jesus Christ to Peter, the chief of his Apostles, later to be martyred when organizing the earliest group of Christians at Rome....According to Matt 16:13-20, when Jesus asked the disciples whom they took him to be, Simon answered for them all that he was the Messiah, the Son of the living God; in reply Jesus pronounced him blessed because of this inspired insight, bestowed on him the Aramaic name Cephas (= 'rock'), rendered Peter in Greek, and declared that he would build his indestructible church on 'this rock', and would give him 'the keys of the kingdom of heaven' and the powers of 'binding and loosing' ....
"[In the first half of Acts]...Peter was the undisputed leader of the youthful church. It was he who presided over the choice of a successor to Judas (1:15-26), who explained to the crowd the meaning of Pentecost (2:14-40), who healed the lame beggar at the Temple (3:1-10), who pronounced sentence on Ananias and Sapphira (5:1-11), and who opened the church to Gentiles by having Cornelius baptized without undergoing circumcision (10:9-48). He was to the fore in preaching, defending the new movement, working miracles of healing, and visiting newly established Christian communities...