Question

What’s a computationally sane way to, given a natural number n, generate a random number that is relatively prime to n?

I’m willing to sacrifice some randomness and coverage of all possibilities for speed. That is, if I only ever hit perhaps 75% of the possible (smaller) relative primes, that’s fine.

Answer 1

in simple words:

unsigned random_prime(unsigned n){
     unsigned r = rand(), t;
     while ((t = gcd(r, n)) > 1)
         r /= t;
     return r;
}