The Greek word agenealogētos appears only once in the New Testament (Hebrews 7:3) to describe Melchizedek, the mysterious priest-king of Salem. The word is formed from the alpha-privative a- (not) + genealogeō (to record a genealogy), meaning literally 'without recorded descent.' It does not necessarily mean he had no parents, but that his priestly authority was not derived from any lineage — making him a type of Christ, whose priesthood is eternal and not inherited.
The author of Hebrews makes a careful argument from silence: Melchizedek appears in Genesis 14 with no mention of father, mother, beginning of days, or end of life. This literary fact is theologically freighted — Melchizedek functions as a type of the eternal Son, who holds his priesthood not by hereditary succession but by the power of an indestructible life (Hebrews 7:16). Without father or mother, without genealogy, without beginning of days or end of life, resembling the Son of God, he remains a priest forever. Christ's priesthood is not of this world's order — it is eternal, superior, and unending.