Melchizedek's priesthood

“Without father or mother, without genealogy, without beginning of days or end of life, like the Son of God he remains a priest forever.” Hebrews 7:3
The writer of Hebrews makes several references to Melchizedek, including all of chapter 7, even though he is only mentioned twice in the Bible (Gen. 14 and Ps. 110:4). Melchizedek was a priest-king who met Abraham when he returned from defeating the four kings who had taken his nephew Lot captive. Melchizedek pronounced a blessing over him, and Abraham gave him a tenth of the plunder he had recovered. Then the story ends; except for Ps. 110:4, which announces that Messiah would be a priest forever in the order of Melchizedek. It is this point that the writer picks up on.
The book of Hebrews is written to Jewish believers. They were familiar with the Levitical priesthood, which obviously traced back to Levi – and thus being completely separate from the royal line, which traced back to Judah. It was impossible for someone of the Levitical priesthood to be a king. Jesus the Messiah is both our King of kings and high priest – but not of the Levitical order. He is of an earlier order, that is superior (as evidenced by the fact that Abraham, the ancestor of Levi, paid a tithe to Melchizedek).
Heb. 7:3 has led to some confusion – because we don’t understand Hebrew logic. The Scriptures give us no record of Melchizedek’s origin or his death. This doesn’t mean that he didn’t have a father and mother, or that he didn’t die. But these details being absent invoke the idea of eternity, and paint a picture of Jesus as our eternal high priest.