Exodus 12:
29 At midnight the LORD struck down all the firstborn in Egypt, from the firstborn of Pharaoh, who sat on the throne, to the firstborn of the prisoner, who was in the dungeon, and the firstborn of all the livestock as well.
Apparently, Pharaoh's firstborn was to inherit the throne. Does the fact that Pharaoh was alive afterward mean that he was not the firstborn?
The topic "Firstborn, Firstling" from the Insight on the Scriptures touches on this issue:
The firstborn came into considerable prominence at the time that Jehovah delivered his people from slavery in Egypt. Among the Egyptians, the firstborn were dedicated as sacred to the sun-god Amon-Ra, the supposed preserver of all the firstborn. The tenth plague that Jehovah brought upon the Egyptians served to discredit this god and showed up his inability to protect the firstborn. By obeying God’s instructions concerning the slaying of a lamb and the splashing of its blood on the doorposts and upper part of the doorway of their houses, the Israelites did not lose their firstborn in death, whereas all the firstborn of the Egyptians, of both man and beast, were slain. (Ex 12:21-23, 28, 29) Evidently the firstborn son of each household is meant in most cases and not the head of the household, even though he may have been a firstborn. Pharaoh himself was probably a firstborn and yet his life was not taken. However, it may be that not every Egyptian household had a literal firstborn son (the married couple being childless or the firstborn son having already died), and in view of the statement at Exodus 12:30, “there was not a house where there was not one dead,” the destruction could have included the chief one in the house occupying the position of firstborn. [bold mine]
And as Nigel mentioned in his comment, it is possible that Pharaoh's father may have already passed away and therefore headship now becomes Pharaoh's and the title of "firstborn" falls on his son.
[All scripture quotations from the New World Translation of the Holy Scriptures (Study Edition)]
The text in question does not answer that question. Also, the matter of establishing exactly which Pharaoh was the one God sent Moses to, is not as simple as most people suppose. If he could be categorically identified, then his lineage could be checked and it would be clear if he was a firstborn son, or not. But I don't want to delve into that, as the point of the Exodus account is to show why God kept this Pharaoh alive till shortly after the slaying of the firstborn - whoever that Pharaoh was. Before Moses pitched up at the Pharaoh's court with Aaron, his brother, God had stated,
"But I know that the king of Egypt will not let you go unless a mighty hand compels him. So I will stretch out my hand and strike the Egyptians with all the wonders that I will perform among them. After that, he will let you go" (Exodus 3:19-20 NIV Emphasis mine).
By the end of the 9th plague, this Pharaoh still had not let God's people go. So, the 10th one was inevitable. However, please note that God had foretold that after all God's wonders, this Pharaoh would then let the people go. Logically, this Pharaoh had to still be alive after the end of the 10th plague.
It's reasonable to assume that he was a firstborn son himself, but he didn't "get off" with the final plague on Egypt's firstborns, for God did strike him dead only a few days later, after he'd let the people go. Pharaoh followed in hot pursuit, seeing the Hebrews cross the Red Sea, then charged in after them, only for God to pile the heaped-up waters on top of Pharaoh and his army, once all the Hebrews were safely across.
The killing of all Egypt's firstborns that night when the obedient firstborns of the Hebrews were spared, could be said to be the pen-ultimate act; the killing of Egypt's 'supreme' firstborn - that Pharaoh - was the ultimate act of judgmental plague the nation of Egypt suffered. With his death at God's hand, the plague on the firstborns ended.
EDIT. Source ref. for claim that God struck Pharaoh dead: Exodus 14:1-28 & 15:1-10 in conjunction with Psalm 106:7-11 Notes on Ex.14:17-18 re. which chariots (with drivers) were drowned, from The Companion Bible which notes the differences of singular and plural : “chariots. Heb. singular chariot. Note the alternation. | Pharaoh (sing). |His host (pl.) |Pharaoh’s chariot (sing.). |His horsemen (pl.).
According to the definition of firstborn given by Merriam Webster, we have the following:
Definition of firstborn : first brought forth : ELDEST
And in hebrew we have some verses with בְּכוֹר֮ (firstborn):
וּכְנַ֗עַן יָלַ֛ד אֶת־צִידֹ֥ן בְּכֹר֖וֹ וְאֶת־חֵֽת׃
Or in english ESV of Genesis 10:15:
15 Canaan fathered Sidon his firstborn and Heth,
To be more sure, we quote a Esau being the firstborn of Isaac:
אָנֹכִי֙ עֵשָׂ֣ו בְּכֹרֶ֔ךָ עָשִׂ֕יתִי כַּאֲשֶׁ֥ר
Or in english ESV of Genesis 27:19 we see:
19 Jacob said to his father, “I am Esau your firstborn. I have done as you told me; now sit up and eat of my game, that your soul may bless me.”
So Pharaoh wasn't a firstborn son since he wasn't killed by the Creator, however he was a firstborn father. But it doesn't say son or father, it says only firstborn in Exodous 12:29, so we can comprehend that the firstborn referred here is truly the firstborn child, and also, in Exodus 12:12 it doesn't say to smite men, it says those born from men (מֵאָדָ֖ם):
וְעָבַרְתִּ֣י בְאֶֽרֶץ־מִצְרַ֘יִם֮ בַּלַּ֣יְלָה הַזֶּה֒ וְהִכֵּיתִ֤י כׇל־בְּכוֹר֙ בְּאֶ֣רֶץ מִצְרַ֔יִם מֵאָדָ֖ם וְעַד־בְּהֵמָ֑ה וּבְכׇל־אֱלֹהֵ֥י מִצְרַ֛יִם אֶֽעֱשֶׂ֥ה שְׁפָטִ֖ים אֲנִ֥י יְהֹוָֽה׃
Naturally, a good question would be that, if every person is born of a man, how can it be that he won't smite men? This is simple, when someone says for example, Luke is the firstborn of Heli, we think that it means Luke is the son of Heli giving it a sense of childhood, the same way when we say the son of the man. In reality, it says that the Lord will smite all those who are "from" Egypt (this is, to to be familiarized with the egyptian culture and living it), not living in Egypt, but why to use "בְּ" instead of "מִ"? Well, this is simple, when we say "from" it gives the sense we are talking about the origin of someone, however it the verse, it says also that prisioners would have also been smitten by the Lord. So the expression בְּכוֹר֮ בְּאֶ֣רֶץ מִצְרַ֒יִם֒ means those living as they were from the land of Egypt.
Using 1 Kings 6:1, Judges 11:26, and Acts 13:20, the Exodus likely happened around 1446 BC. The likely pharaoh would be Amenhotep II who was not a firstborn son nor was his successor Thutmose IV (see Dream Stele).
