I have based my calculation on the Jewish calendar, particular the Jewish Era. So today (year 2007), the Jewish Era would be the year 5767; in our time of 2000, it would be the year 5760 of the Jewish Era. This Jewish Era indicated that the Creation of the World and the Creation of Adam was 5767 years ago, ie 3767 BCE.
From the Jewish Era, I can work out when each patriarch was born and died, from Adam to Jacob, using the Genesis. That's how I calculated the timeline of the patriarchs, which you can find on my website Dark Mirrors of Heaven.
This how I calculated when the Flood happened, 2104 BCE, which is 1656 years after Adam's creation (Jewish Era or JE). Noah himself was born 1056 years after Adam's Creation (JE), thus he was born on 2704 BC. Since Noah was 502 when Shem was born (thus 1558 Jewish Era or 2202 BCE), 2 years after God's warning and instruction on building the Ark. Thus Shem was 98 at the time of Flood and 2 years later Arpachshad was born. So if Shem lived another 500 years as stated in 11:11, then his death would happen 2158 year in the Jewish calendar, ie 1602 BCE.
My calculation of Jacob's birth put him in 2108 Jewish Era, which is 1652 BCE, thus Shem's death happened after 50 years after Jacob's birth.
It stated that Sarah was 10 years younger than Abraham (born in 1948 JE or 1812 BCe), so she would have to born on 1958 JE or 1802 BCE. So if she died at age 127, it would be then 2085 JE or 1675 BCE, which is 23 years before Jacob was born.
Leaving out the BCE or JE (Jewish Era) for the moment, I think you did some miscalculation between Shem's birth to Jacob's birth.
you say that Noah was born 2704 B.C the birth of Noah was
2970 B.C.E. Gen. 5:28, 29. Lamech his father was in his 182nd year when Noah was born.
3152 B.C.E. Birth of Lamech Gen. 5:25
3339 B.C.E. Birth of Methuselah Gen. 5:21
3404 B.C.E. Birth of righteous Enoch Gen. 5:18
3896 B.C.E. Birth of Seth Gen. 5:3
4026 B.C.E. Adams creation Gen. 2:7
Dates mark the time at which events occur. The Bible expresses dates in relation to the lifetime of individuals, the period during which certain rulers were in office, or other notable events. It contains the only complete chronology reaching back to the time of Adams creation. Bible chronology also pinpointed in advance the time when certain important events in the fulfillment of Gods purpose would take place. The Gregorian calendar, which is now popular in much of the world, did not come into use until 1582. In secular sources there is disagreement on dates given for events in ancient history. However, certain key dates, such as 539 B.C.E. for the fall of Babylon, and hence 537 B.C.E. for the Jews return from captivity, are well established. (Ezra 1:1-3) Using such dates as starting points, it is possible to express in terms of current calendars the dates for ancient Biblical events.
1881 B.C.E. Death of Sarah Gen. 17:17; 23:1
2018 B.C.E. Birth of Abraham Gen. 11:26, 32; 12:4