According to Paul, Melchizedek had no genealogy?

There is no record of his father or mother or any of his ancestors--no beginning or end to his life. He remains a priest forever, resembling the Son of God. (Hebrews 7:3)

How comes Paul being a student of rabbi Gamaliel did not know Melchizedek was Shem? In Judaism it is taught that Shem was Melchizedek who Abraham met.

And Malchizedek: The Midrash Aggadah (Targum Jonathan, Ned. 32b, Mid. Ps. 76:3) states that he was Shem, the son of Noah (Rashi commentary on Genesis 14:18)

He asked Melchizedek1See Nedarim 32b, where Melchizedek is identified with Shem, the son of Noah., ( Orchot Tzadikim 14:19)

When Abraham returned from the war, Shem, or, as he is sometimes called, Melchizedek, the king of righteousness, priest of God Most High, and king of Jerusalem, came (Legends of the Jews 1:5:119)

identification of Shem with Melchizedek occurs in the Talmud (loc. cit. in this note), and see Buber’s note 18 on p. 30 of the Midrash Agadah, cf. also Pal. Targum and Jer. Targum on Gen. xiv. 18, (Pirkei DeRabbi Eliezer 8:4)

This goes to show Paul had no clue of the traditional view of Shem. And to make matters worse for Paul, Shem did have a genealogy his father was Noah and mother Naamah. How could Paul assume making up such a lie about Melchizedek will go unnoticed?

Paul was not the student of rabbi Gamaliel and nor was he aware of who Melchizedek was. Paul have deceived millions of Christians till now who believe Melchizedek resembled the son of god? Little do they know Paul lied. Melchizedek was none other than Shem.