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"Obviously a 0.5% difference over 3 billion base pairs is 15 million, not 3 million."

And that is the point I've tried to make in all these exchanges.
.5% equates to 15 million DNA differences, not 3 million, and yet the only solid number I've seen regarding Neanderthals is 3 million base pair differences.

In everything else we agree -- 15 million for Neanderthals is the number we might expect. It's just that I haven't seen it reported yet. When I do, then will concede the point.

And your larger point is also correct -- that these numbers can be more complicated than it might at first seem.
An example of that is the question of "copy number" which turns out to increase intra-human genetic diversity from .1% to .5%.

So it is important that we know which numbers we are talking about before we start throwing them around.

But finally, let me suggest to you a possible reason why the reports are telling us that Neanderthal DNA is only 3 million base pairs different from human DNA.
This could be the case, couldn't it, even if our common ancestors lived 500,000 years ago -- if there was significant interbreeding between those last living Neanderthals and some of our earlier human ancestors.

Wouldn't a bit of trogloditic hanky-panky tend to reset the genetic clocks on both sides? ;-)

I find it much more likely that some journalist wrote down that there were 3 million base pair differences on average among humans, and misreported it as being the difference between humans and neanderthals; and that mistake got repeated. Nowhere in the original science reports did I see this number, and I looked.

As anyone with a calculator can tell you a 0.5% difference over 3 billion base pairs is 15 million not 3 million. Making the report that a 99.5% difference between humans and neanderthals adding up to 3 million base pair difference an obvious error.

Journalists. They don't know much about science, and apparently they cannot do math either.

What WAS reported in actual science journals, unfiltered by journalists, was that the human neanderthal similarity is 99.5%, and using the same criteria, human similarity is around 99.9%.

This is what one would expect when all the data supports humans sharing a recent common ancestor within the last 100,000 years, while neanderthals split some 500,000 years ago. And those are the numbers from actual science papers from actual scientists.