In ancient Jewish traditions Melchizedek is often thought to be Shem, the son of Noah. Melchizedek is a title meaning “king of righteousness,” even though it is also used as a proper name. A modern writer examined the question of whether Shem and Melchizedek could be the same person and concluded that, while we cannot say for sure, the possibility is clearly there. He said:
“Let us examine first what we know about Shem. Although the Bible names Shem as the eldest son of Noah (Gen. 5:32), modern-day revelation places Japheth as the eldest (Moses 8:12). Both reports, however, are harmonious in naming Shem as the progenitor of Israel and in the fact that the priesthood descended through Shem to all the great patriarchs after Noah (1 Chron. 1:24–27). In this patriarchal order of priesthood, Shem stands next to Noah. He held the keys to the priesthood and was the great high priest of his day.
“Living contemporary with Shem was a man known as Melchizedek, who was also known as the great high priest. The scriptures give us the details of Shem’s birth and ancestry but are silent as to his ministry and later life. Of Melchizedek, however, the opposite is true. Nothing is recorded about his birth or ancestry, even though the Book of Mormon states that he did have a father (Al. 13:17–18). Concerning his ministry and life we have several interesting and important facts (Gen. 14:18–20; Heb. 7:1–4; Al. 13:17–18).
“All of this provokes some questions and calls for answers. Were there two high priests presiding at the same time? Why is the record silent concerning Shem’s ministry? Why is nothing known concerning Melchizedek’s ancestry?
“Because of this state of knowledge on our part, many Saints and gospel scholars have wondered if these men were the same person. The truth is, we do not know the answer. But an examination of the scriptures is fascinating, because it seems to indicate that these men may have been one and the same. For example, here is the case for their oneness:
“1. The inheritance given to Shem included the land of Salem. Melchizedek appears in scripture as the king of Salem, who reigns over this area.
“2. Shem, according to later revelation, reigned in righteousness and the priesthood came through him. Melchizedek appears on the scene with a title that means ‘king of righteousness.’
“3. Shem was the great high priest of his day. Abraham honored the high priest Melchizedek by seeking a blessing at his hands and paying him tithes.
“4. Abraham stands next to Shem in the patriarchal order of the priesthood and would surely have received the priesthood from Shem; but D&C 84:5–17 says Abraham received the priesthood from Melchizedek.
“5. Jewish tradition identifies Shem as Melchizedek.
“6. President Joseph F. Smith’s remarkable vision names Shem among the great patriarchs, but no mention is made of Melchizedek.
“7. Times and Seasons [15 Dec. 1844, p. 746] speaks of ‘Shem, who was Melchizedek....’
“On the other hand, there is a case for their being two distinct personalities. Many persons believe D&C 84:14 is proof that there are perhaps several generations between Melchizedek and Noah. The scripture says, ‘Which Abraham received the priesthood from Melchizedek, who received it through the lineage of his fathers, even till Noah.’
“If it does turn out that Shem and Melchizedek are the same person, this scripture should prove no stumbling block, because it could be interpreted to mean that priesthood authority commenced with Adam and came through the fathers, even till Noah, and then to Shem.” (Alma E. Gygi, “Is It Possible That Shem and Melchizedek Are the Same Person?” Ensign, Nov. 1973, pp. 15–16)