- Dick, I'm confused.

I'm assuming that your notation p(n) means the nth prime, so for example

p(25) = 97, the 25th prime. So if we let k=5, then does your formula say:

The first 25 primes will be exactly distributed as follows:

5*(5+1) primes between 1 and (p(25)+1)/2 and the remaining 5*(5-1) primes

will be distributed between ((p(25)+1)/2+1) and p(25)

OR

30 primes between 1 and 49 and the remaining 20 between 50 and 97?

This is not true, (but perhaps you're missing a factor of 2, because there

are indeed 15 primes between 1 and 49 and 10 primes between 50 and 97).

Tom

-----Original Message-----

From: Dick Boland [mailto:richard042@...]

Sent: Wednesday, January 03, 2001 4:19 PM

To: primenumbers@egroups.com

Subject: Re: [PrimeNumbers] Goldbach

Hello,

Yes I can. The distribution function is simply stated as follows,

For any integer k>4, the first k^2 primes will be exactly distributed as

follows:

k*(k+1) primes between 1 and (p(k^2)+1)/2, and the remaining k*(k-1) primes

will be distributed between ((p(k^2)+1)/2+1) and p(k^2).

The way I discovered it was by creating a mathematical model based on "if

Goldbach's Conjecture were not true, what properties must the first (lowest

2*g) exception have?" I narrowed this down to a proof that it must have the

property that there can only be k^2 "odd primes" up to 2*g and that they

must be distributed k*(k+1) "odd primes" below g and k*(k-1) "odd primes"

between g & 2*g.

But before you numerically reach the highest "odd prime" < 2*g that must

represent a (k^2)th odd prime, you have just passed the (k^2)th prime in

light of including "2" as a prime. So the (k^2)th prime, which is an exact

point in the distribution of primes occurs one prime before the (k^2)th odd

prime. What you find is that because primes are distributed in this manner,

you can never restore the balance needed for an exception. Or more

obviously, you can never develop enough order, enough compositeness, to

support an exception to the conjecture.

As for my claims, I have toned them down and I am more comfortable now that

I understand and have taken steps to protect myself. Which is a major

concern of mine because this is my ticket to transform my life into the

profession for which I seem to have been born. I haven't worked this hard

to be left in the dust and have others take the credit. It may sound harsh,

but I didn't mean it to put anybody off, quite the opposite, I am seeking

help to allow this work to see the light of day and to support me so that

the rest of what I am capable of proving can also see the light of day.

-Dick Boland

omega@... wrote:>

thing I found to finally prove it is "THE" prime number distribution

> I have rigidly proven Goldbach's Conjecture. It's amazing because the

function. Did this really escape everybody?>

Hello Dick,

I really dont know what to think of this. My first thought is that its a

rather early 1 April post after reading your claims in the beginning...

Can you explain cq summarize for the mere mortals on this list what THE

prime number distribution function is and how you discovered it?

W

--

http://www.plex.nl/~reney/primepage.html

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The Prime Pages : http://www.primepages.org - From: Milton Brown

Date: 12/21/05 16:35:16

To: Werner D. Sand; primenumbers@yahoogroups.com

Subject: RE: [PrimeNumbers] Goldbach

These messages about Goldbach's Conjecture are not

supposed to be to this mailing list (also the Riemann Hypothesis).

There are separate mailing lists for these.

Kermit says.

Milton! You surprise me.

Goldbach's conjecture IS about prime numbers. It's doesn't matter that

there exist mailing lists specifically about Goldbach's conjecture.

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