Peter is mentioned more than the other apostles. Actually, he is mentioned 155 times alone, whereas the other apostles are mentioned a combined 130 times.
When the apostles are named, Peter is almost always mentioned first. (Mark 1:36; 3:16; Luke 6:14-16; Acts 1:3)
Peter is the first to confess the divinity of Christ. (Matt. 16:16, Mark 8:29; John 6:69)
Only Peter walks on water. (Matt. 14:28-29)
Jesus says that Satan as sought the apostles, but He prays for Peter alone, that his faith not fail so that he could confirm his brethren. (Luke 22:31-32)
Only Peter's death is foretold by Jesus. (John 13:36; 21:18)
Only Peter is told that he has received a divine revelation. (Matt. 16:17)
The tax collector approaches Peter as the representative for Jesus to collect the temple tax. (Matt. 17:24-25)
Peter usually acts as spokesman for the apostles. (Matt. 18:21, Mark 10:28, Mark 11:21 among others)
Peter is the only one who speaks at the Transfiguration, and is again mentioned first going up the mountain. (Luke 9:28;33)
Only Peter is given the keys, the sign of authority. (Matt. 16:19)
Although John arrives at the tomb first, he waits to let Peter enter first. (Luke 24:12, John 20:4-6)
Peter is confirmed as leader of the apostles when the angel says that Jesus was resurrected. (Mark 16:7)
Jesus tells Peter to feed His sheep. (John 21:15-17)
Peter is the one who says that a successor to Judas must be chosen. (Acts 1:15)
Peter gives the first preaching (Acts 2:38) of the early Church, and also performs the first healing (Acts 3:6-7). Only Peter's shadow is mentioned as healing. (Acts 5:15)
Peter is shown exercising authority in the early Church. (Acts 5:3 and Acts 8:20-23)
When the first council of Jerusalem is held to debate the issue of circumcision for the gentile, there is much disputing, however, when Peter speaks, then the multitude is silent (Acts 15:12). Barnabas and Paul speak in support of what Peter has declared (Acts 15:12). Finally, James says that he agrees with Peter and provides Scriptural support for what Peter declared (Acts 15:13-14).
Paul visits Peter before beginning his ministry. (Gal.1:18)
Paul also mentions Peter as having seen Jesus first after his Resurrection. (1 Cor. 15:4-8)
Peter is the only apostle to have his name changed. St. Francis de Sales writes:
When Our Lord imposes a name upon men he always bestows some particular grace according to the name which he gives them. If he changes the name of that great father of believer, and of Abram makes him Abraham, also of a high father he makes him father of many, giving the reason at the same time (Gen 17:5) . . . The imposition of the name in the case of Saint Peter is no small argument of the particular excellence of his charge, according to the very reason which Our ¬ord appended: Thou art Peter, etc.
But What name does he give him? A name full of majesty, not common, not trivial, but one expressive of superiority and authority, like unto that of Abraham himself. For if Abraham was thus called because he was to be the father of many nations, Saint Peter has received this name because upon him as upon a firm rock was to be founded the multitude of Christians.
Our Lord himself is by excellence called the rock, because he is the foundation of the Church, and the corner-stone, the support, and the firmness, of this spiritual edifice: and he has declared that on Saint Peter should his Church be built, and that he would establish him in the faith: Confirm thy brethren. (Luke 22:32)
St. Frances de Sales has an excellent letter on Jesus versus Peter as the foundation of the church. Since that point was discussed extensively in a previous comments section, I am planning to type it up in its entirety and post it as a follow-up in the next day or two.
For other Pope related questions, see our previous post, Papal Ponderings.