The evidence is here:
Christ, the Son of God wrote nothing and used quotes from the OT, as He established His Church and explicitly made four promises to Peter alone, and this is what the Sacred Scriptures teach us:
“You are Peter and on this rock I will build My Church.” (Mt 16:18)
“The gates of hell will not prevail against it.”(Mt 16:18)
I will give you the keys of the Kingdom of heaven.” ( Mt 16:19)
“Whatever you bind on earth will be bound in heaven.” (Mt 16:19) [Later to the Twelve].
“Strengthen your brethren.” (Lk 22:32)
“Feed My sheep.”(Jn 21:17).
St Matthew, 28:
“All power is given to me in heaven and in earth.  Going therefore, teach ye all nations; baptizing them in the name of the Father, and of the Son, and of the Holy Ghost.  Teaching them to observe all things whatsoever I have commanded you: and behold I am with you all days, even to the consummation of the world.”
Peter is conspicuously involved in all the Church’s important “firsts.” Peter initiated the election of the first successor to an Apostle ( Acts 1:13-26). Peter preached the first sermon at Pentecost (Acts 2:14), and received the first converts (Acts 2:4 1). Peter performed the first miracle after Pentecost (Acts 3:6-7), inflicted the first punishment upon Ananias and Saphira (Acts 5:1-11), and excommunicated the first heretic Simon the magician (Acts 8:2 1).
“So great fear came upon all the Church and upon all who heard these things. And through the hands of the apostles many signs and wonders were done among the people. And they were all with one accord in Solomon’s Porch. Yet none of the rest dared join them, but the people esteemed them highly.” (Acts 5:11-13).
Peter is the first Apostle to raise a person from the dead (Acts 9:36-4 1). Peter first received the revelation to admit Gentiles into the Church (Acts 10:9-16), and commanded that the first Gentile converts be baptized (Acts 10:44-48).