Primes seem to me to be more of an information theoretic concept than a number concept. Primes are the simplest way to encode specific kinds of graphs that una

Primes seem to me to be more of an information theoretic concept than a number concept. Primes are the simplest way to encode specific kinds of graphs that unambiguously encodes all sub-graphs. If you try to come up with a bit-representation that is equivalently rich it becomes difficult to think of one that is as simple yet preserves the semantics of the factorization tree. So I guess my point is that the factorization tree of numbers is the fundamental concept, and it's information theoretic. Primes happen to be an encoding of that fundamental concept into integers, but if we found an equivalently rich representation using a different encoding, we might understand primes better. I doubt that the quirks of the encoding has anything to do with the fundamental concept however.