Find duplicate value in large amount of data

I must test an application that generate random keys. Keys are generated with the state of the system. There is 1,7668470647783843295832975007429e+72 states possible. The state change is pseudo random. How can I find the first duplicated value state of the system?

I have made some tries, but i'm far of the solution. Now I use sqlite to stock the data because I catch an out of memory exception if I try to do it with the system memory. With sqlite it's very slow.. I currently use Sqlite with only a text field (primary key) containing the state of the system.

I'm searching for an idea on how to find the first duplicated value generated bye the system. Thanks you!