How to test a random generator

Question

I need to test a random number generator which produces numbers randomly. How to make sure the numbers generated are random.

Answer 1

You cannot ensure the numbers are random simply because random numbers are, well, random.

The chances of getting a string of one million consecutive 9's is the same as getting any other specific one-million-long sequence. The one thing you can check for is correct distribution over a large sample set. Run a sizeable test and work out the relative occurrences of each possible outcome.

Over a large enough sample, they should be roughly the same.

One other possibility is to test for non-repeatability. Ideally, random numbers should not depend on the numbers that came before. Very simple (linear congruential) PRNGs will most likely give you the same sequence of numbers eventually but over a large enough set that you probably won't care (unless you're serious about randomness).