Jesus' priesthood was exactly like that of Melchizedek. If “without father or mother” properly describes Melchizedek, then it also properly, and in the same manner, describes Jesus. If "without beginning of days or end of life" means that Melchizedek was never born or died then the same must be true of Jesus. If it means that Melchizedek had no genealogy, it also means that Jesus had no genealogy. This language cannot mean one thing for Melchizedek and something else for Jesus since the comparison is based on similarities. This cannot refer to the men but to their respective priesthoods. Luke records the fact that Jesus had a genealogy which he traces all the way back to Adam.