Checking about 10^10 of them is just about doable as vhcr correctly showed. (I mean it wasn't optimal, but 'leave this running for 400 hours' is far from impossible)
It is 10^10 cases, checking numbers up to 2^(10^10). The numbers themselves are pretty big (~9 gigabytes each if you want to write full binary representation), but nothing that modern computers can't handle.
