Number of ancestors alive in 1600

Consider a person born in 2000.

Approximately how many of their ancestors would have been alive in the year 1600?

First thoughts:
Assuming each parent averaged age 20 when they had your ancestor, that’s 20 generations. 2^20 is a bit over a million.
Population in 1600 was 554 million. Out of those, say 20 million of them were age 20 and eligible to be the final grandparents.

So then the question becomes, how many of those million ancestors are duplicates of each other due to merges in the family tree? I’m guessing more than half (so my guess is 500K were alive), but I’m not sure how to estimate that.

But then I guess there is a chance for their parents and their child to be alive at that moment, so maybe that pushes the count back up to 1 million.

20 seems a little young for the average, although I realize that generations were shorter the further back you go. But it still seems a little short to be average. I’d probably go with 25.

Yep. 25 sounds good or maybe even 30, since it really should be slightly earlier than the mean age of the parents when their children are born, from oldest child to youngest child. Earlier because I assume the older children are more likely to have their own children.