Random.Next() How many iterations before a wrap around occurs?

I'm pretty sure that this will never be an issue, and probably one that a user would never experience, because the scope of random numbers of any given seed is too big, possibly a few trillion calls to Random.Next(). However, I'm still curious, exactly how many iterations can any given seed generate a random number before its scope is fully exhausted and it wraps back around to generating the same numbers again?

As an example:

Suppose you have an array consisting of eight integer indices; during a given iteration the random.Next would fill each indice with a value of 0-31. And the test is attempting to see how long it would take to generate a perfect array of all 31's.

Mathematically, the odds are roughly 1 in 1,099,511,627,776 per iteration to yield a perfect array of all 31's. However, this is assuming that the C# Random number generator could even make it to the projected range of 1 trillion iterations without wrapping back around on itself.

So, to sum up my actual question, could the Random class achieve the test that I have presented? Or would it reach a half-way mark and just doom itself to failure regardless of how many iterations it goes through>

I should also mention that I am currently running a testing mechanism that is trying to achieve this. So far, this is the current report, which is displayed every minute:

##### Report #####
Elapsed Simulation Time: 00:49:00.1759559
Total Iterations: 20784834152
Perfect 8 Success: 0
Failure: 20784834152
##### End Report #####