Each uniform random number generator - pseudo or real - produces an uniformly distributed output numbers only in a given range.

Usually, this range is [0, 2^n-1], i.e. 2^n consecutive numbers.

Often, a different range is needed. As long as this subrange is of form [k, 2^m+k-1] (m <= n) i.e. 2^m consecutive numbers, it's easy to scale: simply mod the pRNG output by 2^(n-m) and add k. The mod means in fact to take the lowest m bits of the pRNG output (it does not need to be mod, it can be any similar operation, i.e. any m bits of the pRNG output will do).

But, for any other form of scaling, care must be taken. If you simply mod the output of pRNG by any number which is not power of two, you will add some bias to some of the output numbers, so the output is not distributed perfectly uniformly anymore. It is easy to calculate the difference and it's upon you how will you cope with it (including accepting the difference if it's small enough).

A typical extreme example is a pRNG outputting numbers in the [0, 3] range uniformly; if you mod the result by 3, you will get twice as many 0s than 1s or 2s.

JW