Revisions to make after Goldbach, Levy's, and other conjectures
Note in the introduction the similarity between Levy's conjecture and our primes. The only difference between ours is that mine stipulates p,q be consecutive.
The "are they necessarily consecutive?" question can remain unchanged.
The next question "every have a unique p,q pair", let it be related to levy's conjecture and the graph of the number of ways an odd integer can be written as 2p+q _without_ p,q consecutive. State that forcing p,q be consecutive results in primes that can only be written in this one way. Perhaps if we look at all the numbers generated, not only the primes, are they all made of unique p,q pairs? My guess is yes. Namely because p,q are monotonic increasing. Duh…okay, so maybe this paragraph should say "this is an obvious result because p,q are monotonically increasing which means that there's no way that one number could be made in any other way". Maybe look at the patterns of these numbers.
Likely the only interesting result from this paper is the distribution leveling out to 0.1.
The paragraph that really needs changing is the c=2a+b paragraph. This needs to be changed to say that this is the expected result via Goldbach's weak conjecture and it is also just a specific form of levy's conjecture because levy's conjecture says that all odd numbers are of that form. It doesn't seem like we can say anything about the uniqueness of p,q for primes of this form because we assume that levy's conjecture has been investigated enough to find any patterns for one, and it just doesn't seem like it based on the graph.
Just focus on consecutive numbers, you're just looking for specific instances of golbach and levy that maybe would elucidate patterns in their conjectures.