Did Joseph Have More Children?
The Torah writes (Exodus 1:5):And all the souls that came out of the loins of Jacob were seventy souls; and Joseph was in Egypt already
And the sons of Joseph, who were born to him in Egypt, were two souls; all the souls of the house of Jacob, that came into Egypt, were threescore and ten.
We do not find that Joseph had other sons except for Menashe and Ephraim
You should know that Joseph had more children besides Menashe and Ephraim(see also Rashbam and Ramban, and Sefer Mayim Rabim)
(I have also heard in the same of Rabbi Simcha Baer that this explains the sudden shift in numbers for the two tribes of Ephraim and Menashe during the travels in the desert. The shift happened because of the other sons of Joseph who shifted from one of their brother's tribes to another.)
What was Pharaoh's daughter's name?
The Torah writes (Exodus 2:10):And the daughter of Pharaoh came down to bathe in the river; and her maidens walked along by the river-side; and she saw the ark among the flags, and sent her handmaid to fetch it.
and his wife Hajehudijah bore Jered the father of Gedor, and Heber the father of Soco, and Jekuthiel the father of Zanoah—and these are the sons of Bithiah the daughter of Pharaoh whom Mered took.
But did Bithiah give birth to him? Yocheved did, only Yocheved gave birth to him but Bithiah raised him which is why he is called by her nameSimilar connection is cited in the Talmud (Megillah 13a):
Why is she called "Hajehudijah"? Because she threw off idol worship as it says "and the daughter of Pharaoh went down to bathe in the river" and Rabbi Yochanan said: to wash herself from the idols of her father's house
The Holy One Blessed is He said to Bithiah the daughter of Pharaoh: Moses was not your son and you called him your son, so you are not my daughter but I will call you my daughter as it says "these were the sons of Bithiah the daughter of Pharaoh" - daughter of G-d
However, Targum Rav Yosef (Chronicles II 8:11) identifies the wife of King Solomon also as Bithiah, daughter of Pharaoh
Similar, so does the Midrash (Vayikra Rabbah 12:5):
Rabbi Adin said: All the seven years that Solomon was building the Temple, he did not drink wine. Once he built it and married Bithiah the daughter of Pharaoh, that night he drank wine...
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