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You're correct. The correspondence just seems to be due to some bound on the prime gap for arithmetic progressions (or perhaps something even more trivial that I'm missing). A curs…

For fixed n, a block (x,y) contains the numbers n/2 y^2-n/2 y + yz + x for all 0 <= z < n.

It also doesn't reduce the time to O(1). Each of the ranges is of size O(2^(N/2)) for an N bit prime, so it's really not useful at all.

No, this won't help with finding primes. As they noted, the pattern for ranges of size k only holds for k lines. So to find a prime of length N (on the order of 2^N), we need to ha…