http://en.wikipedia.org/wiki/German_tank_problem

How to estimate # of products from observed serial numbers. Let be the number of samples and be the maximum serial number. Then, . Because underestimates , we compensate it by adding the number of missing samples between adjacent observed samples. Also, -1 because we don’t count sample itself when considering missing samples.

Given that, here’s a story on estimating the # of XBox: Xbox Serial Number Statistics