Finding the (probable) maximum of a large set of integers *without* iterating over all of the values
Tricky. 

As an approximation, assume that the number n is in the set with a probability p (n), and the sum of p (n) over all integers n is finite, so we may guess that the set is finite. 

You'd have to check enough values n to make some reasonable assumptions about p (n), and then based on those assumptions make a reasonable guess about the upper bound. 

But let's say that p (n) = $1 / n^2$. The probability that there is any element n ≥ N is about 1/N. So 10 is an upper bound with probability 90%, 100 is an upper bound with probability 99% and so on. On the other hand, your checks will likely show that 1 is an element and find no others. p (n) could be any of a gazillion of possible probabilities. 

Your chances are much better if you have some knowledge about the distribution.