Harristotelian Logic

I've given the conciser sieve form of my prime counting function to dramatically show how clear it is that certain people are ignoring important mathematical research.

The LaTex won't be processed but hopefully some of you who use LaTex will be able to see what it is anyway.

With natural numbers x and n, where p_i is the i_th prime:

:<math>P(x,n) = x - 1 -\sum_{i=1}^n {(P(x/p_i,i-1) - (i-1))}</math>

where if n is greater than the count of primes up to and including <math>\sqrt{x}</math> then n is reset to that count.

Here's an interesting tidbit, you can SEE the equivalent to the above in a specific range in what is called Meissel's Formula:

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

where it is P_2(x,a).

That is the form when

x/p_i < i - 1

as then P(x/p_i, i-1) = pi(x/p_i).

So the actual mathematical reality is that my prime counting function in its sieve form in a specific range is equivalent to a key piece of Meissel's Formula.

Now I figured out my prime counting function as a thinking exercise a few years back, and have had to argue, and argue, and argue with mathematicians about it ever since as the real world is not that people celebrate your discoveries in the math world, they try to ignore them because they didn't make them.

That community is the one you don't understand which is why I'm trying to educate you with easily checkable facts.

Notice how posters swarm over these threads as I create them, babbling nonsense to block out the facts?

Read through those threads and see the same names over and over again, and consider, how many of those people are actually acting alone?

Top mathematicians can ignore me, but how can they be sure that maybe some of you might not pick up on these ideas and start asking uncomfortable questions?

So why wouldn't they have an attack squad out here on Usenet to protect them?

[A reply to someone who wanted to know how James could say that he was being ignored, since his result was published on the Internet and it was acknowledged as correct.]

It is one of the shortest prime counting functions known:

With natural numbers x and n, where p_i is the i_th prime:

:<math>P(x,n) = x - 1 -\sum_{i=1}^n {(P(x/p_i,i-1) - (i-1))}</math>

where if n is greater than the count of primes up to and including <math>\sqrt{x}</math> then n is reset to that count.

And in that form, also one of the fastest.

Because of that unique form it can be fully mathematicized into a summation of a partial difference equation:

If <math>y\le\sqrt{x}</math> then

:<math>P(x,y) = \mathrm{floor}(x) - 1 -\sum_{k=2}^y {((P(x/k,k-1) - P(k-1,\sqrt{k-1}))( P(k,\sqrt{k}) - P(k-1,\sqrt{k-1})))}</math>

else <math>P(x,y) = P(x,\sqrt{x})</math>.

In that form, it doesn't need to be given a list of primes because it uses a partial difference equation, and yes, there is a partial differential equation that follows from it.

All of that sounds like exciting mathematics to me. Lots of places where there is uniqueness and a clear route to a partial differential equation connecting the discrete to the continuous.

Mathematicians ignoring it is like if physicists ignored…um, I don't know.

But mathematicians don't just ignore my research, some of you come on Usenet and lie about it, manipulating newsgroups and telling them bogus math.

There has to be a reason for that behavior.

Simplest reason is that you're con artists who are protecting your con. You know if you properly acknowledge my research your fraud will be outed and you'll lose a money source, so you fight it.