The Greek verb genealogeō (γενεαλογέω) means to trace or reckon one's descent, to register a genealogy. It appears only once in the New Testament (Hebrews 7:6), where the author notes that Melchizedek's genealogy is not traced — making him typologically significant as a priest who points beyond the Levitical system.
The absence of genealogeō for Melchizedek in Hebrews 7 is theologically profound. In a culture where priestly legitimacy depended on documented genealogy, Melchizedek stands apart — 'without father or mother, without genealogy, without beginning of days or end of life' (Hebrews 7:3). He foreshadows Christ's eternal priesthood, which is not inherited through human descent but bestowed by divine oath. Jesus's priesthood transcends all genealogical qualification — it is eternal, indestructible, and perfect.