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Take a look at the maps there are for the area:
You meant Galilee, Samaria and Judea. Those are indeed sometimes referred to as "provinces" in English. How long would it take to tour these compact subdivisions on foot?
Modern Israel subtends about 8000 square miles. New Hampshire, with a similar aspect, is bigger. A leisurely hiker can visit each of the three main public college campuses in New Hampshire (Plymouth in the north, Keene in the southwest, and Durham in the southeast0 in under a month (~ 77 hours time on foot, according to Google maps.)
Your cited source is
Acts 8. That doesn't help you much. The chapter begins with Paul approving of the stoning of Stephen in or near Jerusalem, in Judea. According to 7:58, Paul's role in the stoning was to watch the cloaks of the pitchers while they killed the deacon.
Then chapter 8 says that Way-people fled to locations in Judea (outside of Jerusalem) and Samaria. There's nothing about a third province, and there's nothing about Paul or anybody else pursuing anybody outside of Judea, where Paul already was, watching the cloaks.
However, Judea isn't a province where Paul was "notiorious." What does Paul say? "I was personally
unknown to the churches of Judea that are in Christ." (
Galatians 1: 22, emphasis added). "They only heard the report: 'The man who formerly persecuted us is now preaching the faith he once tried to destroy.'"(1: 23).
The only additional scrap of information about Paul in
Acts 8 is that Paul entered an unspecified number of houses, dragged out of those houses an unspecified number of people, and handed them over to unspecified prison authorities (8: 3).
There is action set in Samaria in chapter 8, but none of it involves persecution, much less persecution by Paul. There appear to be no churches to persecute yet, and the involuntary flight away from Jerusalem may have introduced Wayism into the area. There's nothing about the preachers in Samaria being harassed by anybody.
Acts 8, then, shakily documents what can be accomplished in an afternoon, and none of Paul's busy afternoon is set anywhere except Judea. No wonder, then, that few in the pews of the Judean churches had heard of Paul until his few deeds, but mighty intentions, were explained to them.
With Chapter 8 in the bag, then, we are two provinces light of places where Paul performed any acts of persecution, and three provinces light of Paul being notorious there as a persecutor. You have yet to produce a source for your statement "Saul Paul became infamous across three Roman provenances (
sic) for his persecution of Christians. "
