Harristotelian Logic

With my story and my research it is easy to get perspective on just what has to be happening by considering any number of areas, but I'll give you one new one as over the weekend I thought about twin primes, and had a basic simple idea:

If x is prime, then if you loop through all the primes up to sqrt(x+2), and find that none of them divide x+2, then x+2 must be prime, or to put it another way, if

x+2 = 0 mod p

for each prime p up to sqrt(x+2) is NOT true, then x+2 is prime.

Turns out the probability that x+2 is prime relative to a given prime p, is easy as it's just

(p-2)/(p-1)

and you msy be wondering where I get that, when it's just 1 - 1/(p-1) as p-1 is the count of non-zero residues modulo p, like for 5, 1, 2, 3 and 4 are the residues modulo 5. So you take the odds that you get a residue that would mean x+2 is divisible by p, and just subtract that from 1 to get the odds that it will NOT be divisible by p.

And you just do that for each prime up to the sqrt(x+2), and multiply them together to get a probability that if x is prime, x+2 is prime, or, the probability given that x is prime that you have twin primes.

See:
http://mymath.blogspot.com/2006/07/twin-primes-probability_30.html

Now that is so easy you'd think it'd have been part of the mathematical literature a long time ago, but it looks like, scarily, mathematicians just got close, but never quite figured it out, as see

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

where you can see (p-1)/(p-2) in some of the formulas they show, but I haven't seen the simple explanation for why it's there, and it gets worse.

So if x is prime the probability that x+2 is prime is given by

prob = ((p_j - 2)/(p_j - 1))*…*(1/2)

where j is the number of primes up to sqrt(x+2), and p_j is the jth prime.

And if you read my post you'll see I even found a way to relate this to Goldbach's conjecture, where I've just kept going with this REALLY simple idea, as why just consider 2? Why not consider an arbitrary even prime gap g?

Next thing you know, Goldbach's is right in front of you.

But why is ANY of this new??!!!

And can it be ignored? I hope not, but consider all the research I have at this point.

Like, why would they ignore any of my research, like my short proof of Fermat's Last Theorem?