To extrapolate on your point for those interested: The analogy I'd give is from physics. Understanding the prime number structure is like understand how an arb

To extrapolate on your point for those interested: The analogy I'd give is from physics. Understanding the prime number structure is like understand how an arbitrarily complex 3-dimensional shape will interact with another equally arbitrarily 3-dimensional complex shapes (let's just assume rigid-body interaction here). But it should be intuitively obvious that starting with the question you want to answer "how do arbitrarily complex shapes interact" (the analog, in our example, to "how are arbitrary primes structured") is too big an undefined question to answer directly. Maybe somebody will be able to do it, but most likely it will be solved by breaking it into smaller, incomplete, but accurate models that though comparing and contrasting (e.g. why do circles interact differently than squares) and combination (e.g. I know circles interact, I know how squares interact, I can now define a grand circle/square unification theory that describes how circles and squares interact) . So, you break the problem down into questions like "how do circles interact?", "how do squares interact?", "how do one-dimensional shapes interact?", "2D?". By identifying subclasses of the overall uber problem it's possible to solve a hard larger problem. Back to the primes example, each different metric for defining a relationship between primes effectively defines a new class of primes that can be probed to figure out why they act in the way they do and how they are distributed. Each class of prime is a (probably, but not necessarily) incomplete yet accurate model for how all primes operate overall.