I'm not even sure how you get to 4000 years old from biblical literalisim.
Edit: going strictly by the biblical account, Adam lived to 930 years, and Noah 950. IIRC, their lives did not overlap. Jesus lived 2000 years ago. A whole bunch of stuff happens in between Noah and Jesus. So even if you're working strictly from the bible, how the hell do you get 4000 years?
The original calculation (adding up all the ages in the genealogies in the Bible) was done a few hundred years ago, but all the young earth creationists I saw put the start at 4000 A.D., so 6000 years ago.
There is a very old Jewish Holiday which celebrates new year on a calendar starting with the creation of the Universe, only about 5000+ years, but even that is obscure af.
Ussher calculated 4004BC as the start of the universe, which would be about 6000 years ago.
That's my point. Most YEC point to 6000 years. Even within their own framework, I don't see how you get to 4000 years. My best guess is they saw 4004BC and forgot that 1 BC was about 2000 years ago.