The Apostle Paul was truly blessed by Christ and was arguably the greatest of the Apostles. He had the honor of seeing Heaven (Acts 14:19, 2 Cor. 12:1-6), he wrote two-thirds of the New Testament, and he was selected to be the final Apostle (1 Cor. 4:9 and 15:8). God also chose to reveal six mysteries to Paul:
1) The Mystery of Godliness - 1 Timothy 3:16
2) The Mystery of the Indwelling Christ - Colossians 1:27
3) The Mystery of the Body of Christ - Ephesians 5:30-32
4) The Restoration of Israel - Romans 11:25
5) The Mystery of Iniquity - 2 Thessalonians 2:3-8
6) The Rapture - 1 Corinthians 15:51-55
The Greek word "mustérion" is used in each of the verses listed above. Mustérion implies knowledge that can only be gained through revelation. We would call this a secret or something unknown. In modern English, Paul would have said "allow me to tell you a secret". One of these secrets, or mysteries, was the Rapture.
"Behold, I shew you a mystery; We shall not all sleep, but we shall all be changed, in a moment, in the twinkling of an eye, at the last trump: for the trumpet shall sound, and the dead shall be raised incorruptible, and we shall be changed." - 1 Corinthians 15:51-52
The phrase "at the last trump: for the trumpet shall sound" has caused many to speculate what Paul was referring to. One thought is that Paul was referring to the Feast of Trumpets. Eddie Chumney, in his book The Seven Festivals of the Messiah, stated that this phrase was a common Jewish idiom. While it is possible that the Rapture may occur on this Feast, I personally reject this theory for two reasons.
*SIDE NOTE*
I am giving multiple reasons for my rejection of these theories because it is on the testimony of two or three witnesses that a verdict should be established (Deut. 19:15). Please do not form doctrine solely off of one Bible verse!
The first reason is that there is a reward for those that look for His appearance in 2 Timothy 4:8. In this verse, the Greek term "agapaó" is used which denotes an active and on-going love or desire. Basic human nature is one of complacency until the arrival draws near; however, this type of love is the opposite of that. It symbolizes a person that is actively looking for ways to fall deeper in love.
The second reason is found in 1 Thessalonians 5:1. Paul stated to this church, "...of the times and the seasons, brethren, ye have no need that I write unto you". The term that Paul used for "seasons" was "kairōn". Kairōn means when "things are coming to a head" i.e. culminating. If Paul was referring to the Feast of Trumpets, he would have used the term "giortí̱" which means "feast" or "holiday".
Another theory for what Paul was referring to is found in Revelation chapter 11 when the seventh trumpet of judgment sounds. While there are trumpets mentioned in both verses, I reject this theory as well.
The first reason is because Revelation was given to the Apostle John around 90 AD. 1 Corinthians was written around 55 AD. Not only were the trumpet judgments not revealed to Paul, but they weren't even revealed for another 35 years!
The second reason is that the final trumpet judgment signals Christ's return to the earth (Rev. 11:15). That would place the Rapture at the time of Jesus' return sort of like a ping-pong effect.
The third reason is that the trumpet judgments are blown by an angel (Rev. 11:15).
The final reason that I reject this theory is because "the last trump: for the trumpet shall sound" is not an actual trumpet. Look at the following Rapture passages carefully:
"For the Lord himself shall descend from heaven with a shout, with the voice of the archangel, and with the trump of God: and the dead in Christ shall rise first: Then we which are alive and remain shall be caught up together with them in the clouds, to meet the Lord in the air: and so shall we ever be with the Lord." - 1 Thessalonians 4:16-17
"After this I looked, and, behold, a door was opened in heaven: and the first voice which I heard was as it were of a trumpet talking with me; which said, Come up hither, and I will shew thee things which must be hereafter. And immediately I was in the spirit: and, behold, a throne was set in heaven, and one sat on the throne." - Revelation 4:1-2
Revelation and 1 Thessalonians both describe Jesus' voice as that of a trumpet! Paul was saying that God will shout for His Church one final time and that is the Rapture.
In each dispensation (see lesson here), God called people to Him. Keeping in mind that the Church Age is Romans through Philemon, Paul referred to God calling us 44 times in his epistles. You can find the verses in Romans, 1 Corinthians, Galatians, Ephesians, Colossians, 1 and 2 Thessalonians, and 1 and 2 Timothy.
I do not know when the Rapture will take place, but did Paul say that we can know when it is near.
And we are in that time right now (see parable of the Fig Tree lesson).