Shem had a mother and a father, a birth and a death, Melchezidic had neither genealogy and no beginning of days nor death.. read with your own eyes, take the scriptures word for it not mine.
Hebrew 7:1-3
For this Melchisedec, king of Salem, priest of the most high God, who met Abraham returning from the slaughter of the kings, and blessed him; To whom also Abraham gave a tenth part of all; first being by interpretation King of righteousness, and after that also King of Salem, which is, King of peace; Without father, without mother, without descent, having neither beginning of days, nor end of life; but made like unto the Son of God; abideth a priest continually.
Nathan is an apologetic, the Septuagint timeline has Shem dying before Abraham, this goes against the Rabbinic anti-Christian belief that Shem met Abraham..
Shem is from the tribe of Levi so Jews teach that because Jesus was from the tribe of Judah then he can not be the new High Priest, yet in Hebrews we learn that Melchezidic is an eternal, without genealogy nor descent etc... so Shem is not Melchezidic
[ For this Melchisedec, king of Salem, priest of the most high God, who met Abraham returning from the slaughter of the kings, and blessed him;
2 To whom also Abraham gave a tenth part of all; first being by interpretation King of righteousness, and after that also King of Salem, which is, King of peace;
3 Without father, without mother, without descent, having neither beginning of days, nor end of life; but made like unto the Son of God; abideth a priest continually.
4 Now consider how great this man was, unto whom even the patriarch Abraham gave the tenth of the spoils.
5 And verily they that are of the sons of Levi, who receive the office of the priesthood, have a commandment to take tithes of the people according to the law, that is, of their brethren, though they come out of the loins of Abraham:
6 But he whose descent is not counted from them received tithes of Abraham, and blessed him that had the promises.
7 And without all contradiction the less is blessed of the better ]
As for melchizedek having no father or mother, genealogy, etc.
I believe that ole sh'aul is referring to the titles of the priesthood. Hence the distinction he gives concerning the lesser preisthood of levites
Not sure how you came to the conclusion that shem was, "from the tribe of levi".
Would you mind explaining