Prime numbers thin out. We have very good estimates of how they thin out. We also know that gaps between primes can get arbitrarily large. And we cannot predict

Prime numbers thin out. We have very good estimates of how they thin out. We also know that gaps between primes can get arbitrarily large. And we cannot predict when the next prime will happen without huge computations. And large primes have a use, e.g. cryptography (although, who knows when we'll have a use for such a large one). Having a list of primes is also very useful for empirical evidence for many conjectures in number theory. None of these things are true about natural numbers in general.