I continue to see minor errors and typos throughout the posts I’ve made. So far I haven’t found any fatal flaws in the reasoning, but the minor errors can be fairly irritating. Hopefully they don’t detract too much from the arguments being presented.
I’m more of a big picture, concepts guy, a bit lazy with the details sometimes. 🙂
A brief philosophical segue that’s been waiting to get out, now that I have managed to get the Kn formulae figured out in the last post.
I keep reading about randomness in the distribution of primes. There’s nothing at all random about the distribution of primes; their pattern is fully, completely, 100% deterministic. It just appears stochastic when we stand back and look without an appreciation for the underlying order.
One number gives birth to the entire infinitude of prime numbers, the humble number 2. Simple repetitions of 2, from 0 to infinity, followed by a simple recursive rule, generate the whole beautiful complex of prime numbers, prime twins and prime k-tuples of all shapes and sizes, each of which extend to infinity themselves.
At the headwaters of the primes, we let the 2s flow outward, bounding down, eliminating other natural numbers as composites, leaving potentially unique numbers behind. The first natural number not eliminated, 3, becomes the next prime, and is also let flow outward, bounding away, stripping away composites, leaving behind possible primes. An infinite recursion of this process yields the infinite set of prime numbers, which can be collapsed back to their simple roots in the number 2.