Generate a serial number whose probability to be guessed is less than 1/1000

Question

I'm asked to generate random serial numbers whose probability to be guessed is less than 1/1000. How to find out in which range should these numbers be ?

Answer 1

For purposes of clarity and completeness, I'll move the comments into an answer.

The simplest model that satisfies your constraint is to pick a number between 0 and 1000 (inclusive). As there are 1001 possible choices, the chance of guess is $\frac{1}{1001}$ which is less than $ \frac{1}{1000}$.

Clearly, any set of at least 1001 distinct integers also suffices.