Assume a human generation is 25 years. Each generation you go back the number of ancestors one has doubles. 3500 years would be 140 generations. If every ancestor was different, there would have to be 2^140 or 1.4 x 10^42 people in the world in 1500 BC, somewhat more than most estimates. The obvious conclusion is that many, many ancestors overlap.

An article describing the common SET of ancestors from 100,000 years ago:

Since all humans descended from a common set of ancestors that lived in Africa about 100,000 years ago, there have been relatively few generations in human history compared to older species. As a result, the human haplotype blocks have remained largely intact and provide an unbroken thread that connects all people to a common past and to each other. Recent research indicates that about 65 to 85 percent of the human genome may be organized into haplotype blocks that are 10,000 bases or larger.

National Human Genome Research Institute

And an article explaining better than I have about the MOST RECENT common ancestor:

If this is a bit mind-boggling, it’s just the tip of the iceberg. Dr. Mark Humphrys, a professor at the School of Computing, Dublin City University, has analyzed the results of Chang’s work as well as numerous other academic papers and come up with some startling conclusions. According to Humphrys, everyone in the world is descended from the Egyptian royal house (ca. 1600 B.C.), and almost everyone in the world is descended from Confucius (ca. 500 B.C.). Moreover, he claims, nearly every Muslim, Jew, and Westerner is descended from the Prophet Muhammad (ca. A.D. 600). I don’t have the mathematical kung fu to evaluate these claims thoroughly, but they certainly are thought-provoking. Even more scary: the thought that thousands of years from now, I could be the ancestor of everyone alive!

ITOD

Dr. Chang's paper