Well, taken those k's, how big is the chance that each number of a k still unfactored differs by a multiple of 16 (of 2^4) to other numbers of that k?

I've just found out that the n's even all differ by a multiple of 12!
I don't think that this is just coincidence.

I *guess* that only numbers of this special form "survive" sieving by very small numbers (< 100). But I don't know, hence I'm asking...