The dating of roughly 4,000 BCE (by various researchers of the Bible) for the date of the creation of Adam is based up the Hebrew OT, but based upon the Greek Septuagint Adam was created about 5,500 BCE years (when using an Ussher style method of tabulation). That is because a some of the numbers in the Greek text are larger than those in the Hebrew test. There is strong evidence of the Christians wrote the NT were using the Greek Septuagint Bible as their OT Bible instead of the Hebrew OT Bible.
Furthermore, a number of Bible scholars say that the Hebrew words translated as "son" in our Bibles don't only pertain to sons, but also to grandsons and great-grandsons, and great-great-grandsons (in other words, meaning 'male descendant') - and that thus the chronology of ancestries skips many generations. That then allows for a Bible based dating of the creation of Adam to even about 10,000 BCE to 12,000 BCE!. As a result that interpretation corresponds well with the year modern science says the most recent age
ended and also about the time that agriculture began. Furthermore, they make the Bible based date of the creation of Adam a little bit closer to what modern science science says is when our species evolved into existence.
http://www.accuracyingenesis.com/chronology.html for some ideas along these lines, though those source are not necessarily authoritative. I do not necessarily agree with all that those sources say.