Is there proof of the Savior or the Living Prophet?

I was reading in Mark and noticed that a testimony of a centurion was mentioned. In pondering why this testimony made it, I became convinced that it was a powerful one. Consider how many executions the centurion likely witnessed. He probably had seen dozens if not hundreds of executions or deaths. However, this one was clearly different. Here's the man's words about Jesus:

39 ¶And when the centurion, which stood over against him, saw that he so cried out, and gave up the ghost, he said, Truly this man was the Son of God.

It was likely the logical conclusion of the centurion that this man was the Son of God.

On a related note, I was reading Thomas Monson's biography on a plane this week. My boss was sitting next to me and asked what I was reading. I said I was reading the Prophet's biography and explained we believe he is a prophet, just like Moses and Noah. He said, "but I bet there isn't validation or proof of this." I responded, "oh, there's plenty of proof. You can pray and ask God if he is a prophet, think about his works and teachings, do what he says, study the topic. All of these things are proof he is a prophet." With the things of God, just like the things of man, it is true that when impressive things happen that lead to good outcomes, it's worth figuring out why. In my case, as I have followed church leaders, the outcomes have consistently been wonderful. As this happens over and over again, it becomes very obvious that the Church is true and the Prophet is a true Prophet of God.

Just like the Roman centurion recognized Jesus as someone different, based on the man's vast experience, I recognize truth based on my experiences. It's only logical for me to believe Thomas Monson is a prophet. Everything I've seen shows it's true.