This is just an optical illusion. The "structure" of primes is that they are the atoms with which we can build the natural numbers (via multiplication). There

This is just an optical illusion. The "structure" of primes is that they are the atoms with which we can build the natural numbers (via multiplication). There are just enough primes (and they occur just often enough) to do this. My question would be, are there things analogous to primes in other types of number systems, particularly useful ones.