It's not arbitrary at all! We know that primes themselves get rarer and rarer (density of primes < N is ~1/log(N)), so it is natural to ask whether the gaps between them must also necessarily increase and, in general, how are they spaced.
We know the primes are rich in arithmetic progressions (and in fact, any set with positive “upper density” in the primes is also rich in arithmetic progressions).
So we do know that there are 100,000,000,000! primes that are equidistant from one another, which is neat.