I was surprised they didn't discuss why there were 48 prime candidates co-prime to 2, 3, 5, 7 below 210; and 8 co-prime to 2, 3, 5 below 30; and 480 below 2310.

I was surprised they didn't discuss why there were 48 prime candidates co-prime to 2, 3, 5, 7 below 210; and 8 co-prime to 2, 3, 5 below 30; and 480 below 2310. I've been calling it the larial for years, but it's the primorial minus 1 at each step, i.e. (2-1)×(3-1)×(5-1)×(7-1) = 48. Or the fact that there will always be 1 number coprime to n (and lower primes) that is non-coprime to n+1 in the first n columns for every row on the table, which is where the Larial comes from. I discovered this stuff independently nearly a decade ago and didn't share because it didn't seem novel to anyone I discussed it with. And I have dated Google drive documents and Gmail emails to prove it. But I suspect it isn't worth proving. This math does make pretty music though: https://on.soundcloud.com/juyxv https://on.soundcloud.com/juyxv