Genesis 15:13-14 Then He said to Abram: "Know certainly that your descendants will be strangers in a land that is not theirs, and will serve them, and they will afflict them 400 years. And also the nation whom they serve I will judge; afterward they shall come out with great possessions."Seems pretty clear, right? But...Acts 7:6-7 But God spoke in this way: that his descendants would sojourn in a foreign land, and that they would bring them into bondage and oppress them four hundred years. 'And the nation to whom they will be in bondage I will judge', said God, 'and after that they shall come out and serve Me in this place'.
Exodus 12:40 Now the sojourn of the children of Israel, who lived in Egypt, was 430 years. And it came to pass at the end of the 430 years - on that very same day - it came to pass that all the armies of the LORD went out from the land of Egypt.So the Exodus was 430 years after the offering of Isaac (the unconditional covenant). But wait!Galations 3:15-17 Brethren, I speak after the manner of men? Though it be but a man’s covenant, yet if it be confirmed, no man disannulleth, or addeth thereto. Now to Abraham and his seed were the promises made. He saith not, And to seeds, as of many? but as of one, And to thy seed, which is Christ. And this I say, that the covenant, that was confirmed before of God in Christ, the law, which was 430 years after, cannot disannul, that it should make the promise of none effect.
Acts 13:17-21 The God of the people of Israel chose our fathers; he made the people prosper during their stay in Egypt, with mighty power he led them out of that country, he endured their conduct for about forty years in the desert, he overthrew seven nations in Canaan and gave their land to his people as their inheritance. All this took about 450 years. After this, God gave them judges until the time of Samuel the prophet.So, 450 years from "Chosing the fathers" to inheriting the land. The land was inherited 40 years of wandering plus 10 years of conquest after the Exodus.
Jacob, father of physical Israel was chosen at birth. This makes only 270 years in Egypt - consistent with Exodus 6:18-20. Kohath (already born when they entered Egypt, Genesis 46:11) lived to be 133, Amram 137, and Moses was 80 at the Exodus (Exodus 7:7). This makes at most 350 years - more like 80 years less than that, since people then were having kids at 40.
So, we have to make Jacob's journey to Egypt 130 years later - or 1718 BC. Which puts Joseph clearly within the 14th dynasty of Egypt.