Looking only at genetic code, is it possible that there have ever been two genetically identical people who are not twins (or clones)? How many medically distinct human beings can their actually be?

I’m assuming that we’re only talking about biologically modern human beings. So the genes that make us human cannot be eligible for variation.

If we don’t include environmental factors and non-DNA genetic material, what is the actual number of genes that can vary from one person to another? Do we even understand the human genome well enough to make this kind of calculation?

I’m assuming from combinatorial math that it’s more humans than can ever exist through the course of the entire universe. But what is the actual number? If those genes are varied at random, how many people will it take before they say a 50% chance that two of them are identical? For example, it only takes 23 people to have a 50% chance that at least two of them have the same birthday.

Edit: I found an interesting article about the complications with trying to calculate this number. The number seems to be on the order of 10^(tens or hundreds of thousands)