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Sojourn of Israel in Egypt
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How long were the Israelites living in Egypt?
The Bible says that the Israelites sojourned in Egypt for 430 years. Exodus 12:31-42
"the length of time that the Israelites lived in Egypt was 430 years". Exodus 12:40
The New Testament also refers to this 430 years. Galatians 3:17 says “ The law, introduced 430 years later, does not set aside the covenant previously established by God and thus do away with the promise. “ Genesis 15:12-16 Because of this it is traditionally believed that the 430yrs commenced with the promise being given to Abraham 215yrs before Jacob and his family moved to Egypt.  
The result of this is that some scholars believe that Jacob moved to Egypt only 215 years before Moses lead the Israelites out of Egypt (The Short Sojourn).
Other scholars believe that the Jacob's family numbering about 70, move to Egypt 430 years before the Exodus (The Long Sojourn).
When Jacob and his family went to Egypt, the Israelites numbered about 70. When they left Egypt they numbered around 2 million. They needed time time multipy to this number.
Not withstanding this, it is obviously important to know whether the Isralites were in Egypt for 430 years or 215 years so that we know in which dynasty to look for Joseph.
It appears that there were only 3 generations after Levi who was in the original group that went to Egypt, until Moses who was 80 years old when he lead the Israelites out of Egypt. Four Generations in Egypt would make a Long Sojourn unlikely (although their ages do add up to more than 400 years and they may have had children at an old age as did Abraham). It is hard to see how the Israelites would come to number 2 million in 4 generations unless the tribes of Israel had shorter generation times than the Levites. Exodus 1:1-6 Exodus 6:13-26 Numbers 1:1-54 Numbers 2:1-34
Looking at the promise God made to Abraham it would appear that God was telling Abraham that his children would serve as slaves in a foreign land for 400 years and then God would bring them out of that land with great wealth and give them the promised land. Genesis 15:12-16 Acts 7:6-7
The place where Abraham received the promise was Cannan. This is where Jacob was born and returned to before moving to Egypt. In Genesis 15:12-16 & Acts 7:6-7 it is clear that the foreign land where the Israelites would serve as slaves for 400 years did not include Caanan.
The Egyptian Chronology
In order to correlate Egyptian history with the Bible, it is also important to know how the Egyptian dynasties are ordered.
A number of archaeologists such as David Down have suggested that Egyptian history should be revised as it is now known that many Egyptian dynasties ran in parallel and some have been counted twice! What's more, it was common practice for pharaohs to co-reign for a while so the incoming pharaoh could be trained up and be tested.
The traditional chronology with sequential dynasties and sequential pharaohs was derived from the list of pharaohs and the lengths of their reigns left by Mantetho who was a preist in Egypt who had access to the Alexandrian library before it was destroyed.
Archaeologists are in agreement about the dates when Solomon started building the Temple (966BC)and hence the date of the Exodus is generally agreed to be around 1445BC (480 yrs before the building of the Temple 1Kings 6:1 ). There is mounting archaeological evidence to suggest that Moses was born in the 12th dynasty of Egypt when Sesostris III was pharaoh. Moses would have grown up during the reign of Amenemhet III and it is quite likely that Sobekneferu was the Princess who found him in the Nile. Moses would have become the next Pharaoh Amenemhet IV if he had not killed and Egptian official and had to flee from Amenemhet III. He may even have co-reigned with Amenemhet III for a while. When Moses returned to Egypt 40 yrs after fleeing from Egypt, there was a different Pharaoh in charge of Egypt; Neferhotep of the 13th dynasty. Neferhotep was the Pharaoh of the Exodus.
What difference does it make?
People who believe in a 430yr sojourn in Egypt look for Joseph in an earlier dynasty and given the similarities between Joseph and Imhotep, have tended to place Joseph in the 3rd dynasty serving Pharaoh Djoser (Netjeriket).
If the Israelites were in Egypt for 430 yrs as suggested by Exodus 12:40-41 , then the date of Joseph's entry to Egypt can be determined to be around 1885BC. According to the chronology of David Down, this would place Joseph very close to the 3rd dynasty of Egypt where the most likely candidate for Joseph, namely Imhotep, is located.
People who believe in a 215 yr sojourn in Egypt look for Joseph earlier in the 12th dynasty and have nominated Mentuhotep as a possibility.
One of the problems of placing Joseph in the 12th dynasty means that the flood of Noah would most likely have occurred during during one of the earlier dynasties (2450BC) and this is not only out of keeping with the Bible but there is no archaeological evidence of a worldwide flood during any Egyptian dynasty.
Even Manetho, whom most archaeologist regard as the most authoritative source of information on the chronology of Egyptian history, believed that Mizraim and Menes (the first Pharaoh) were the same person.
A complete revision of the Egyptian chronology is required to allow for parallel dynasties running concurrently in the North and the South and also for the common practice of co-regency. The result would be a considerable reduction in the time frame of the Egyptian dynasties.
This would allow historians to look in the right dynasty for archaeological evidence of the Israelites.
If it is true that Joseph and Imhotep were the same person, then the first pyramid (the Step Pyramid in Saqqara) was designed by an Israelite at the begining of Israel's Sojourn in Egypt and if the last of the great pyramids (those of the 12th dynasty) were constructed with a core made from mudbricks which were made by Israelite slave labour, then the Israelites were in Egypt while all of the great pyramids were being constructed. After the Israelites departed from Egypt in the 13th dynasty, lead by Moses (Amenemhet IV), there were not enough slaves left in Egypt to construct pyramids any more. No more large pyramids were built after Moses (Amenemhet IV) lead the Israelites out of Egypt in 1446BC. The Pyramid Age coincides with Israel's sojourn in Egypt. The pyramids would, therefore, have been constructed over a period of around 400 years.
Answering the Atheists who claim that the Bible is a collection of myths
Placing Joseph in the 3rd dynasty and Moses in the 12th dynasties not only fits very well with the archaeological evidence, it fits very well with the Biblical account. It is Egyptian chronology that needs to be revised.
What we know about Biblical characters from the historical records can be used to fill in the gaps in the Biblical record revealing how miraculous, amazing and glorious the Hand of God has been in dealing with mankind.