"Bad date call: That the murder of James and the dispersion was around 47 A.D. Actually it was around 40-42. Herod Agrippa died in 44.
And Saul was consenting unto his death. And at that time there was a great persecution against the church which was at Jerusalem; and they were all scattered abroad throughout the regions of Judaea and Samaria,
except the apostles. (Acts 8:1)
Therefore they that were scattered abroad went every where preaching the word. (Acts 8:4)
The church was scattered abroad. That is the common members. The Apostles, including Peter, continued to make Jerusalem his home. He never moved.
Bad assumption #1: That Peter continued to live in Jerusalem after the dispersion. In all probability he was living in Rome at the time of the Jerusalem Council and came back to Jerusalem to attend it. Had Peter been living in Jerusalem at the time, he would likely have presided over the Council rather than James.
Bad assumption #2: That Peter was living in Antioch during the confrontation with Paul. Galatians 2:11 says "But when Cephas came to Antioch, I opposed him to his face." Sounds like he was just passing through, not living there.
Bad assumption #3: That Peter wrote from Babylon on the Euphrates. This is something only the most benighted would believe, such as those with an agenda to prove that Peter did not live in Rome. Babylon is universally held to be Rome in the Petrine epistle.
So, if Peter left Jerusalem at the time of the dispersion of the Christians (circa 40-42) and moved to Rome where he died (circa 66-67), he would have been there 24-27 years."
Bad calculations on your part. Look again:
Peter didn’t live in Rome, and there is no evidence pointing in that direction.
He lived in Jerusalem for a good part of his life. He was there just before and after Paul’s conversion.
And Saul was consenting unto his death. And at that time there was a great persecution against the church which was at Jerusalem; and they were all scattered abroad throughout the regions of Judaea and Samaria, except the apostles. (Acts 8:1)
Except for the Apostles, including Peter, the rest of the church in Jerusalem was scattered because of persecution. The Apostles remained in Jerusalem.
When the persecution stopped Peter began to travel, more or less as an itinerant preacher.
Then had the churches rest throughout all Judaea and Galilee and Samaria, and were edified; and walking in the fear of the Lord, and in the comfort of the Holy Ghost, were multiplied.
32 And it came to pass, as Peter passed throughout all quarters, he came down also to the saints which dwelt at Lydda. (Acts 9:31-32)
--Lydda is a town between Jerusalem and Caesarea, about 15 miles east of Joppa.
And forasmuch as Lydda was nigh to Joppa, and the disciples had heard that Peter was there, they sent unto him two men, desiring him that he would not delay to come to them. (Acts 9:38)
--15 miles down the road he went to Joppa, and healed Dorcas also called Tabitha.
And it came to pass, that he tarried many days in Joppa with one Simon a tanner. (Acts 9:43)
--It doesn’t say exactly how long he was in Joppa, but he resided there for a while.
There was a certain man in Caesarea called Cornelius, a centurion of the band called the Italian band, (Acts 10:1)
And now send men to Joppa, and call for one Simon, whose surname is Peter: (Acts 10:5)
Then Peter went down to the men which were sent unto him from Cornelius; and said, Behold, I am he whom ye seek: what is the cause wherefore ye are come? (Acts 10:21)
--Now Peter is in Caesarea with Cornelius and his household. He came straight from Joppa.
And when Peter was come up to Jerusalem, they that were of the circumcision contended with him, (Acts 11:2)
--Immediately after the conversion of Cornelius and others in that area, he went straight to Jerusalem to report of these events there.
And he killed James the brother of John with the sword. And because he saw it pleased the Jews, he proceeded further to take Peter also. (Then were the days of unleavened bread.) (Acts 12:2-3)
--Peter is still at Jerusalem. It is probable that the date is ca. 42-44, the king being King Agrippa I.
And when Herod had sought for him, and found him not, he examined the keepers, and commanded that they should be put to death. And he went down from Judaea to Caesarea, and there abode. (Acts 12:19)
--Now Peter is on the move again—From Judea to Caesarea. But now it says, that here he made his abode—his home. He stayed here for awhile.
And certain men which came down from Judaea taught the brethren, and said, Except ye be circumcised after the manner of Moses, ye cannot be saved. (Acts 15:1)
And when they were come to Jerusalem, they were received of the church, and of the apostles and elders, and they declared all things that God had done with them. (Acts 15:4)
And the apostles and elders came together for to consider of this matter. And when there had been much disputing, Peter rose up, and said unto them, Men and brethren, ye know how that a good while ago God made choice among us, that the Gentiles by my mouth should hear the word of the gospel, and believe. (Acts 15:6-7)
--This was an important matter, so Peter came down from Caesarea to Jerusalem to have his say.
And after they had held their peace, James answered, saying, Men and brethren, hearken unto me: (Acts 15:13)
Wherefore my sentence is, that we trouble not them, which from among the Gentiles are turned to God: (Acts 15:19)
--Note: James was not one of the 12. He was the half brother of Jesus who was saved after the resurrection, and was well respected in the community. He was also the same James that wrote the epistle of James. This James is now the pastor of the church at Jerusalem. This is why the responsibility lies on him to make the decision. James hears the report of the Judaizers (legalists), and then of Paul and Barnabas, and then of Peter and others. He takes everything into consideration, and he makes the judgment (sentence). He is the pastor of the church.
Then pleased it the apostles and elders, with the whole church, to send chosen men of their own company to Antioch with Paul and Barnabas; namely, Judas surnamed Barsabas, and Silas, chief men among the brethren: (Acts 15:22)
--Note, that after James gave his decision that it pleased the apostles, as well as the rest of the church. James gave a good decision that was pleasing to all involved.
But when Peter was come to Antioch, I withstood him to the face, because he was to be blamed. (Galatians 2:11)
--This is the next chronological mention of Peter. It is shortly after the Jerusalem Council. He went from Jerusalem to Antioch, and engaged in the very things that they just voted against. He was hypocritical at this point and needed to be rebuked. This could be as late as 52 A.D. There is no indication he had ever been to Rome.
Peter, an apostle of Jesus Christ, to the strangers scattered throughout Pontus, Galatia, Cappadocia, Asia, and Bithynia, (1 Peter 1:1)
--Look who he is writing to. The geographic center of these places is Babylon from where he claims to have written this epistle. We have no reason to doubt him. The Jews had been dispersed, and that is who he is writing to: Christians with a Jewish background.
The church that is at Babylon, elected together with you, saluteth you; and so doth Marcus my son. (1 Peter 5:13)
And account that the longsuffering of our Lord is salvation; even as our beloved brother Paul also according to the wisdom given unto him hath written unto you; As also in all his epistles, speaking in them of these things; in which are some things hard to be understood, which they that are unlearned and unstable wrest, as they do also the other scriptures, unto their own destruction. (2 Peter 3:15-16)
--Even though he had been sharply rebuked by Paul, he recognizes Paul’s writings as actual Scripture.
Between Antioch (52 A.D. and the writing of this epistle, a year or so before his death, ca. 66 A.D) you cannot fit 25 years. In fact you can’t even prove that one year was spent in Rome.
Read Jamieson, Faucett, and Brown’s commentary for more useful information on 1Pet. 1:1.