Harristotelian Logic

So now I have the explanation for how such simple ideas about primes were not explored—mathematicians thought using probability in this way was beneath them!

Some of it is still weird though, like did no one know where (p-2)/(p-1) came from with twin primes?

See: http://mathworld.wolfram.com/TwinPrimesConstant.html

I still find that bizarre. Tell me someone knew!!! Where did they get it from then?

For those who don't know, I recently started mulling over twin primes and noted the obvious thing that if x were prime if

x+2 = 0 mod p

were NOT true for all primes where p was a prime less than sqrt(x+2) then x+2 had to be prime, so you'd have twin primes, and I worked out the simple formula for the probability given x being a prime that x+2 was prime as well, which is where you see (p-2)/(p-1) in MY research.

I kept going and worked out the probability for when x is a natural that x is prime, and still kept going to figure out the probability that a natural x is a twin prime, and kept going to consider arbitrary even prime gaps.

See: http://groups.google.com/group/AboutMyMath

The mystery has been, how could this research be new? The idea is simple enough, so it seems odd that it hadn't been thought of or pursued before.

Well, apparently mathematicians don't like the idea of thinking of primes with probability in this particular way though they will talk about probability in other ways, preferring thing like 1/ln x, so they just had a disdain for the approach!

I am still hoping to get more info on the particulars, especially how close any particular person got in published research, as there was a citation given on sci.math of someone who did use (p-1)/p for the probability of a natural x not having p as a factor.

The disdain of mathematicians for a logical line of reasoning, however, may have allowed a lot of time spent on questions that can only be answered one way, as the reality is that primes behave in this way where they don't have a preference for a particular residue modulo another prime.

So it can be shown that the twin primes conjecture can be proven only one way, and no other line of argument is available to prove or disprove it.

It can be shown then that Goldbach's conjecture cannot be proven to be true.

There is also then a direct link between the primes and ln x in this fascinating way which shows how prime numbers play a role in ALL of mathematics, including with continuous functions.

The logical arguments necessary to make all those connections are not hard.

Like with twin primes, when none of the primes less than sqrt(x+2) are factors of x+2 when x is a prime, then you have a twin prime, trivial. Otherwise you do not. There is no other reason!!! So it is a probabilistic thing.

Goldbach's conjecture works over a lot of numbers because the probability is extraordinarily high that an even composite C can be written as the sum of two primes.

But there is no other reason.

So over infinity it fails, with an infinity of failures, but with a very low likelihood that anyone will ever find a counterexample.

Regardless of the huge arguments that can erupt over these ideas, there is the prime gap formula itself, which should be part of the literature. So no matter what, if it's not already there, if mathematicians are who many of you still apparently think they are, then they MUST accept that formula and add it to the body of accepted human knowledge.

I fear they will fight. So those of you who give a damn about the truth should get ready as these people will be fighting for their professional lives with their backs against the wall.

I fear they will fight, and they will lose, as at this point in time I have more than enough intellectual tools to crush them at will, but things are likely to get very messy as they bring whatever they can against the truth, and the will of the world.