We're getting close. There's way more RAM than that in the world, and a quick search turned up a single machine from a few years ago that was only off by 160x o

We're getting close. There's way more RAM than that in the world, and a quick search turned up a single machine from a few years ago that was only off by 160x or so. Even without relying on the pigeonhole principle though you still have the birthday paradox. As a ballpark estimate, if you have N keys then you'd expect a 50/50 chance of at least one collision with sqrt(N) hashes -- 2^32 for this problem.