Before discussing the uses of random numbers it is useful to have some idea of how random numbers are generated on a computer.
Most methods depend on a chaotic sequence.
The commonest is the multiplicative congruential method which relies on prime numbers. This process generates all integers less than in an apparently random order. After all integers have been generated the series will repeat itself. Thus one important question to ask about any random number generator is how frequently it repeats itself. This property is extremely useful for debugging purposes, but can be a problem when averaging has to be done over several runs.