This is not true. Paul was not a Christian, in fact he even brutally persecuted them. And he claimed to see the resurrected Christ. He also said 500 other people saw the resurrected Christ at one time and most of them were still alive. 1 Cor 15: 5-8
http://www.christiananswers.net/bible/1cor15.html
Christ being seen by 500 people at once could explain the tremendous growth of Christianity throughout the Roman Empire even in the face of possible torture and death. Paul was really putting himself on the line by saying most of the 500 were still alive. Skeptics of the time would certainly be able to track down some of the over 250 witnesses still alive.
DOC, he said that as a Christian. Do you undersand this fact? You are supporting my argument, so why do you lead with "This is not true". The whole point is that someone who was sure of the resurrection would not deny the faith unless you have evidence of someone who did. For someone to attest the resurrection of Jesus they would have to believe that it occurred. For Paul to persecute Christians he necessarily did not buy the idea that Jesus had been resurrected. It was not until he had the visionary experience on the road to Damascus -- of a risen Christ -- that he changed his mind.
As to the "500" -- what? Skeptics would track down unnamed witnesses 20 years after the fact in another region of the Roman Empire? Whatever you're smoking, I'd like some because there is no way anyone could make such an argument soberly or rationally.
This didn't all happen in a high school auditorium where you could look across the room but in a widely spaced area over a long period of time. If someone in Galatia or Corinth did not believe that Paul was telling the truth, do you honestly think s/he would track down the details? Most of the Jews probably thought he was nuts. What, a crucified criminal is the Lord of the Universe? Yeah, right. The logical response for the unbeliever would be -- go screw yourself, I've got work to do.
But let's say that someone did check up on Paul's account. And let's say this person found out that he was wrong. How is such an account going to survive? It has to be copied and re-copied through the ages. There was a concerted attempt to squelch forms of Christianity that did not fit the proto-orthodox creed -- we are lucky to have surviving documents (but we do have them -- and they demonstrate that Christianity was not one creed from very early) -- so what do you think would happen to a document that denied the faith entirely?
Why would anyone even bother? You are looking at this with 21st century eyes after proto-orthodox Christianity won its battle and Christianity has become intwined in the current power structure. In the 1st century there was a completely different perspective.
ETA:
As to the "500" being the reason why the faith spread so quickly, what? The evidence we have is that the faith did not spread quickly in Jerusalem. The city did not convert overnight and become a Christian enclave as one would expect if 500 people witnessed the miraculous right before their eyes (not to mention the dead that emerged from their tombs to walk about the city earlier). The faith spread in the rest of the Roman Empire, from best estimates in peri-Jewish settlements.
Oh, wait, did that happen in Jerusalem or in Galilee? I have trouble keeping up with the instructions -- go immediately back to Galilee, do not depart but stay in Jerusalem. How are we to know where this happened? Paul doesn't say.