Adam failed as a prophet by failing to tell his wife what she needed to pursue holiness (Genesis 3:17).
Adam failed as a priest because he disqualified himself from tending the Garden of Eden (Genesis 3:24). The word עבד used in Genesis 2:5, 15 to describe Adam tending the Garden is used through the rest of the Old Testament to describe priestly duties.
Adam failed as a king because by failing to subdue the serpent, over whom he had been given dominion (Genesis 1:28). This word for dominion רדה is used of kings in 1 Kings 4:24, and of other political leaders elsewhere.
Jesus is a prophet (Acts 3:22-23, 7:51-53). He satisfied the qualifications for this office during His earthly ministry (Matthew 10:40-41, 13:57, Mark 6:4, Luke 4:24, 13:33, John 4:19). He succeeded where Adam failed by telling His wife, who is the church, all she needs to pursue holiness (Ephesians 5:23, 2 Corinthians 11:1-2, Matthew 28:19-20).
Jesus is a priest (Hebrews 5:5-6, 7:11-17, 21, 24, 10:19-21, 1 Peter 2:4-5). If one understands the Epistle to the Hebrews in conjunction with Psalm 110:1-4, Acts 2:34-35, and Matthew 26:64, one necessarily comes to the conclusion that He satisfied the qualifications for this office no later than Pentecost. He succeeded where Adam failed by tending to the church, which is His temple (2 Corinthians 6:16).
Jesus is a king (Acts 5:31, 17:6-7, 1 Corinthians 15:25, Colossians 1:9-17, Titus 6:13-16, 2 Peter 1:11, Revelation 1:5, 2:10, 11:15, 19:15). He satisfied the qualifications for this office at His birth (Matthew 2:2, Luke 1:32-33), and He is stated to be a king elsewhere during His earthly ministry (Matthew 21:5, 28:18, Luke 1:33, John 1:49, 12:14-15, 18:33-37). He succeeded where Adam failed because the serpent is now powerless, weak, and left plotting in vain (Hebrews 2:14-15, Revelation 12:9, 17-16).
Futurism detracts from the prophethood of Jesus. By denying the Olivet Discourse has been fulfilled, opponents of Christ can point to the His most important prophecy unrelated to His resurrection as false. Bertrand Russel did exactly that, focusing on Matthew 24:34. He was not mistaken. The use of "this generation" here doubtless corresponds with the same phrase used in Matthew 11:16, 23:13-39, Mark 8:12, Luke 7:31-32, 11:29, 50-51, 17:25.
Premillennialism detracts from the priesthood of Jesus. He, being permanently in the Melchizedek priesthood, will be enthroned at the right hand of the Father until his enemies are vanquished (Psalm 110:1-4). His last enemy is death (1 Corinthians 5:25-26). If one insists that death will continue for 1000 years or more after Second Coming, one necessarily insists that Jesus' priesthood will be suspended without Biblical precedent.
Premillennialism detracts from the kingship of Jesus. He is the subject of Psalm 2, according to Acts 4:25-28 and Revelation 19:15. Jesus as king has been given the nations, in accordance with Psalm 2:8 and Matthew 28:18, so Satan cannot rule while Jesus rules with a rod of iron in Psalm 2:9. The kingship of Christ is the prerequisite for the Great Commission. "All authority has been given to Me in heaven and on earth. Go therefore and make disciples of all the nations, baptizing them in the name of the Father and the Son and the Holy Spirit," so anyone who believes Satan rules this world and still evangelizes is disobeying the Great Commission.
To believe that Christ is the last Adam, to believe that He has succeeded in every office where Adam failed, to believe an inextricable link between the offices, and to tell others about Him requires that He made accurate predictions of the future which have come to past, that He will serve as priest until death is no more, and that He rules this world we live in right now. I affirm this with every fiber of my being. Do you?