It is doubtful that a prison guard working in a cell dungeon would have ever heard of who this man Jesus was. So if this be so, how could the jailer believe on a savior in whom he had no knowledge of in light of Rom 10:14 ? People take it for granite that the Jailor was talking about spiritual salvation when he sprang in and ask the question but, could he not have been talking about being saved from a be-headment because he thought the prisoners had escaped ? And then Paul used the opportunity to give him an answer of spiritual salvation. In verse 25 it tells us that Paul and Silas prayed and sang songs so, it is possible that the jailor was awakened of his condition at this time. God is able at an instant to reveal himself to man by a word spoken in season while others must hear a lifetime of preaching before they are converted. You have twisted what I posted previously to make it sound like that a man has to have some long drawn out education before he can be saved.
Oh brother, a lame attempt to try to argue this unregenerated man was not seeking God and true salvation. When it comes to scripture or Calvinism, the Calvinist will always choose Calvinism over scripture!
This jailer probably knew exactly why Paul and Silas had been thrown in his jail. We are told that a young woman possessed with a spirit of divination had followed Paul and certain others about, shouting, "These men are the servants of the most high God, which shew unto us the way of salvation".
Finally, after many days of this, Paul became annoyed and grieved with her and cast the spirit out. Her masters who made much money from her were very upset and went to the authorities, and a multitude of men were gathered against Paul and Silas. Paul and Silas were dragged through the streets and beaten.
This would have been "front page news" so to speak, so surely the jailer had heard of Paul preaching the gospel, though he probably had not heard Paul in person and did not fully understand what Paul was preaching.
But one thing he seems to have understood, that Paul was preaching forgiveness of sins, and this man desired to know how he could be saved.
I agree that there are certain things you must know to be saved, but it does not take a great deal of time. Most folks are quite aware they have sinned. And most people are not atheists and believe in God. The gospel is that Jesus is the Son of the true God, who was made flesh, lived under the law without sin, and died for our sins on the cross. After three days he was raised from the dead, and if we place our trust in him, our sins will be forgiven.
As for the thief on the cross, most likely both men had heard of Jesus and were somewhat familiar with him. They were Jews and knew the promise of the Christ or Messiah. The thief who was saved seems to have realized that Jesus was the Christ all of Israel looked for, and cast himself on Jesus's mercy, asking only to be remembered when he came into his kingdom. He received more than that.