> Nobody bothers explaining why the primes are spaced like they are

I take it that means you also haven't taken (m)any number theory classes then ;-). Because people wildly care about that.

This is in a sense the background of another well-known conjecture, the Riemann conjecture...

Fair point, and correct (just one class). Myself, I'm fine with a field being important because well it's a mystery of the universe and well we just couldn't not scratch the itch. But I know that not all askers want answers like that, so I was attempting to dust off the "it's also useful" neurons :)