Sunday, August 03, 2008


My prime counting function

Sieve form of my prime counting function:

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

P(x,n) = x - 1 - sum for i=1 to n of {P([x/p_i],i-1) - (i-1)}

where if n is greater than the count of primes up to and including sqrt(x) then n is reset to that count.

That simple algorithm will count primes out to positive infinity. And yes, it is perfect.

It is the shortest representation of a prime counting function that I've ever seen that is not just brute force i.e. check each natural and see if it's prime.

If you code it, you can easily verify that it works. Just to be sure you understand what I mean, note that P(100,4) = 25 as there are 25 prime up to 100, and P(10,2) = 4, where those primes are 2, 3, 5 and 7, and that [] is the floor() function, so [1.333]=1.

It is in actuality part of one of the most remarkable intellectual finds in human history, and I did the research back in 2002, and for my troubles the mathematical community has given me grief and understanding this story is a lot about understanding the reality of our academic world, and it's relevant here because I am also a Java programmer with the open source project Class Viewer and I fear that some of you completely have the wrong idea about me.

I am not a crackpot. I am a major discoverer who can prove it easily, like with that prime counting function above, and even show you what you have missed, like not getting taught it in school or seeing it in journals or added to references, though I fully informed the mathematical community years ago.

I like simplicity and elegance, which is why my Class Viewer project is so minimalist and doesn't require a lot of instruction.

My research simplifies mathematics.

It simplifies it greatly.

If you do a search on "prime counting function" and read what mathematicians traditionally teach you will get knocked over by complexity.

Complexity gives room for paper, books, lectures and lots more mathematicians doing research in an area than are actually needed.

Don't believe me?

Then, program the prime counting function. Look at what's out there for prime counting functions. Notice mine is not given. Consider that I have been beating the drums on this research since 2002 and try to come up with a better explanation.

That is just one of my more minor results. The others are much bigger and ALL of them are simplifying results.

I've been told by mathematicians that my prime counting function is not important because they don't think it's interesting. But it is the most compact representation of a prime counting function known, other than brute force. It is the ONLY multi-dimensional prime counting function that I know of. And it is a unique find that should at least be cataloged.

But if I let it die, they would let it die. They would let the knowledge be lost if they could, but I will not let them.

The trouble with a lot of people shouting conspiracy all the time is that when you actually are faced with one you can say, it's not possible or it has to be some crazy guy who just doesn't understand, which is why I say: program the algorithm, look over the literature and see.

And if you get really bold, just ask the mathematicians, and then see what happens.

I have six years of experience of knowing what they do, so I have nothing to learn there.

Quite simply, they will disappoint you.

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