One area where was surprised with simple was with prime numbers, as if you look at primes modulo each other, my feeling immediately was, why would they care?
Putting that mathematically is easy and did so, with my prime residue axiom. But before that had done much with my prime gap equation where notice have not talked it much since, and linking to a post made August 2006.
And next public post I find is this one from February 2010, where give my prime residue axiom:
Given differing primes p1 and p2, where p1 > p2, there is no preference for any particular residue of p2 for p1 mod p2 over any other.
Implications seem to move me usually into things dealing with probability. Will admit am not so much into probabilistic things, which is one reason have not talked as much but also is really easy to encapsulate into a small area. It also does lead to discrete results, as you can just do things like count off how many primes should be twin primes for instance within some block of primes.
Also though that ONE idea if true promptly leads to resolutions of big things supposedly unsolved. Like says Twin Primes Conjecture is right and Goldbach's Conjecture is wrong though disappointing there as we're unlikely to ever find a counter-example regardless. So yeah, plenty of reasons there to just not deal with much? Is weirdly potent an arena. SO much wrapped up there.
Am trying to stay away from talking other things, but it is sad to consider what motivations might shift certain people from a basic truth. For me? Have been lucky that my discovery has been disconnected from money. But have wondered about mathematicians who make their money a certain way, as to what might be more important to them? Truth? Or a paycheck? Well enough said on that subject.
And have focused a lot on 3; with p a prime, p mod 3, for all primes greater than is of course 1 or -1; so is the only binary prime residue in that way. Where yeah, why should greater primes have a preference for 1 or -1 modulo 3?
Am like, why would they care? Makes no sense to think a prime would to me. But realize is an area of contention based on research have done. Am NOT a mathematician so am not sure on details much, while have tried to learn in detail in the past from web search.
Talked for a different audience on my blog Beyond Mundane: No prime preference?
It is amazing how much can come with such a simple idea, and lack of prime preference for any particular residue modulo another prime has been put out there before, which I found out with web searches. My thing was to say, is an axiom.
I like that bold.
James Harris
No comments:
Post a Comment