## Prime Number Generator & Goldbach's Conjecture

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• Y all, Prime numbers may be created by: 1. start with a tube with circumference of 1 (unit) and mark a straight line that runs the length of the tube and is
Message 1 of 3 , Apr 13, 2011
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Y'all,

Prime numbers may be created by:

1. start with a tube with circumference of 1 (unit) and mark a straight line that runs the length of the tube and is parallel to the axis of the tube. Place this line in the is Top Dead Centre (TDC) position.

2. on top of the tube, place a ring of circumference 2. mark a point on the ring at the bottom of the ring. this is Bottom Dead Centre (BTC) for the "2" ring (2-ring) and must touch the tube's TDC.

3. rotate the tube 3 turns, so that the tube's line is back to TDC and the 2-ring's mark is now at TDC for the 2-ring.

4. because no rings' mark touches the tube's line at TDC, then 3 is prime and we must add a 3-ring. again, it's marked with a mark at BDC and touching the line at the TDC position of the tube.

4. Rotate the tube (4 rotations in total, so far). the 2-ring's mark is BDC and touching the tube's TDC mark, and the 3-ring's mark is rotated 1/3 rotation from the tube's TDC. because a ring's mark (the 2-ring's BDC) is touching the tube's TDC, 4 is not a prime.

5. rotate the tube 1 more rotation (5 rotations in total, so far). now the 2-ring's mark is in the 2-ring's TDC position. the 3-ring's mark is 2/3 rotated away from the Tube's TDC mark. Therefore, because no ring mark is touching the tubes line at TDC, then 5 is a prime.

6. continue to rotate 1 rotation at a time so that the tube's line is started and stopped at the tube's TDC. Whenever no ring's mark touches the tube's line, that number is prime, and a ring of that circumference must be added on top the tube with a mark at the new ring's BDC position. whenever any number >0 of ring's marks are at BDC and touch the tube's line at TDC, then this number is not prime.

7. Therefore, Goldbach's Conjecture may be restated as, for every integer greater than 3, there exists a prime number "x" clock-wise rotations and "-x" (i.e. counter-clock-wise rotations) from that integer.

Bill Krys

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• On Wed, 13 Apr 2011 16:31:10 -0700 (PDT), Bill Krys ... Hi ! ... that sounds like a version or cousin of
Message 2 of 3 , Apr 13, 2011
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On Wed, 13 Apr 2011 16:31:10 -0700 (PDT), Bill Krys
<billkrys@...> wrote:
> Y'all,
Hi !

> Prime numbers may be created by:
<snip>

that sounds like a version or cousin of
http://en.wikipedia.org/wiki/Wheel_factorization
(I have not enough brain tonight to dig more).

> 7. Therefore, Goldbach's Conjecture may be restated as, for every
> integer greater than 3, there exists a prime number "x" clock-wise
> rotations and "-x" (i.e. counter-clock-wise rotations) from that
> integer.

that's one idea and I have suspected for several years
that the prime wheels will help us prove Goldbach.

I am still working on the "low hanging fruit" (n-uplets
such as twin primes) but my approach does not look suited
to Goldbach. I hope you will make progress, as I'm curious
how you will come up with the right proof construction !

> Bill Krys
Yann
• Yann,   I don t believe you understand my generator. I don t think it directly relates to the Wheel Factorization process. I am not sure if mine is a sieve,
Message 3 of 3 , Apr 14, 2011
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Yann,

I don't believe you understand my generator. I don't think it directly relates to the Wheel Factorization process. I am not sure if mine is a sieve, as I understand a sieve to start with a set of numbers and then sieve out the primes. With my generator, the primes are generated incrementally. However, in a general sense, by selecting only primes to be generated, then I guess one could view it as a sieve, but then again, any prime number generator could be viewed as a sieve and then the meaning of sieve becomes unclear, to me anyway.

What I am working on now is looking at clockwise and counter-clockwise rotations that produce primes on either side of an integer.

Bill Krys

This communication is intended for the use of the recipient to which it is addressed, and may contain confidential, personal, and or privileged information. Please contact the sender immediately if you are not the intended recipient of this communication, and do not copy, distribute, or take action relying on it. Any communication received in error, or subsequent reply, should be deleted or destroyed.

--- On Thu, 4/14/11, whygee@... <whygee@...> wrote:

From: whygee@... <whygee@...>
Subject: Re: [PrimeNumbers] Prime Number Generator & Goldbach's Conjecture
To: "Bill Krys" <billkrys@...>
Date: Thursday, April 14, 2011, 2:32 AM

On Wed, 13 Apr 2011 16:31:10 -0700 (PDT), Bill Krys
<billkrys@...> wrote:
> Y'all,
Hi !

> Prime numbers may be created by:
<snip>

that sounds like a version or cousin of
http://en.wikipedia.org/wiki/Wheel_factorization
(I have not enough brain tonight to dig more).

> 7. Therefore, Goldbach's Conjecture may be restated as, for every
> integer greater than 3, there exists a prime number "x" clock-wise
> rotations and "-x" (i.e. counter-clock-wise rotations) from that
> integer.

that's one idea and I have suspected for several years
that the prime wheels will help us prove Goldbach.

I am still working on the "low hanging fruit" (n-uplets
such as twin primes) but my approach does not look suited
to Goldbach. I hope you will make progress, as I'm curious
how you will come up with the right proof construction !

> Bill Krys
Yann

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