I dont see why one would need to go beyond scripture to prove Peter held some type of authority above the rest.
We can start with the name. Kepha.that alone is significant, since in the old testament only God was called rock.
John 1:42 Jesus looked at him, and said, “So you are Simon the son of John? You shall be called Cephas” (which means Peter *).
when someones name changed that usually meant their status changed. Gen 17:25 No longer shall your name be Abram, * but your name shall be Abraham; * for I have made you the father of a multitude of nations.
Gen 32:28 Then he said, “Your name shall no more be called Jacob, but Israel, * for you have striven with God and with men, and have prevailed.”
2 Kings 23:34 And Pharaoh Neco made Eliakim the son of Josiah king in the place of Josiah his father, and changed his name to Jehoiakim.
Dan 1:6-8 Among these were Daniel, Hananiah, Misha-el, and Azariah of the tribe of Judah. 7 And the chief of the eunuchs gave them names: Daniel he called Belteshazzar, Hananiah he called Shadrach, Misha-el he called Meshach, and Azariah he called Abednego.
we see John and James called the sons of thunder, but they were still called by their names, James and John. only Simon would be called by his new name , Peter.
also significant is when Jesus came to Cesarea Phillipi.
Matt 16:13 Now when Jesus came into the district of Caesarea Philippi, he asked his disciples, “Who do men say that the Son of man is?” this was near the southern foothills of Mt. Hernon were there is a giant wall of rock some 200’ high and 500’ long. Matthew gives us the name of this place because it relates to Peter , whose new name means rock, and also what takes place.
Matt 16:17 And Jesus answered him, “Blessed are you, Simon Bar-Jona! For flesh and blood has not revealed this to you, but my Father who is in heaven. 18* And I tell you, you are Peter, * and on this rock * I will build my church, and the powers of death * shall not prevail against it.
There are some people who try to twist this by giving some elabrate explanation of the greek petros and petra. but the fact is Jesus and the others spoke aramaic, Hebrew was considerd a Holy language and reserved. so the phrase would read " you are kepha and on this kepha i will build my church.” and if thats not enough , then the next verse SHOULD suffice.
Matt. 16:19 I will give you the keys of the kingdom of heaven, and whatever you bind on earth shall be bound in heaven, and whatever you loose on earth shall be loosed in heaven."
to Peter alone he gave the Keys. the term keys to a jewish person would mean AUTHORITY.
Is 22:22 And I will place on his shoulder the key of the house of David; he shall open, and none shall shut; and he shall shut, and none shall open.
Rev. 1:18 and the living one; I died, and behold I am alive for evermore, and I have the keys of Death and Hades.
the Apostles later were given authority to bind and loose, but to Peter alone were given the keys to the Kingdom.
Satan knows to kill the body you must destroy the head. Jesus is the ultimate head of the Church. but Peter is the head of the Church on earth. that is why satan demanded to have him.
Luke 22:31 Simon, Simon, behold, Satan demanded to have you, * that he might sift you like wheat,
and we see in the next verse Jesus commands Peter to strengthen the brethren. Luke 22:32 but I have prayed for you that your faith may not fail; and when you have turned again, strengthen your brethren."
and he commands Peter to lead his flock and feed his sheep.
John 21:15-17
He usually was always named first among the disciples.
Matt 10:1-4, Mark 3:16-19 , Luke 6:14-16 , Acts 1:13
He generally spoke for the others.
Matt 18:21, Mark 8:29, Luke 12:41, John 6:68
He was present at some of the most extraordinary moments
Matt 14:28-32, 17:24, Mark 10:28
at pentecost he was the first to speak
Acts 2:14-40
and the first to heal
Acts 3:6-7
it was to Peter that came the revelation to baptize gentiles
Acts 10:46-48
to this Church Jesus entrusted the Holy Spirit that it would faithfully and without error , concerning faith and morals, hand on the teachings of Christ and truth. the same Church that Jesus said the gates of hell will not prevail agianst, and that he would send the Spirit of Truth to guide it, has always declared Peter the first Pope, or the first head of the Church. or should we believe as some do , that the Holy Spirit took a 1500 year vacation?