Re: There are 2^256 private keys out there: how big is that number?
p.s. a bit nitpick-y but there are 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364140 private keys which is a little smaller than 2256 
I'm trying to understand it but failed. Why not 2^256? They are hashes right? Like strings. All possible combinations. Where is the mistake?
They are not hashes. Public keys are X,Y points on a very large curve which has just under 2^256 points.