## Building Twin Primes II

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• All twin primes after (29,31) are built as 30*k + (11,13) or +(17,19) or +(29,31) Attached is a table for k from 1 to 20 showing their construction. The
Message 1 of 6 , Jun 8, 2005
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All twin primes after (29,31) are built as 30*k + (11,13) or +(17,19) or +(29,31)

Attached is a table for k from 1 to 20 showing their construction.

The assertion is that for every k which is prime, there is at least one
of the 3 additions which produces a twin prime.

(30)k +(11,13) -------+(17,19) ------+(29,31)
=================================
1 -------(41,31) --------(47,49x)------- (59,61)
2p -----(71,73) --------(77x,79) -------(89,91x)
3p ----(101,103) -----(107,109) -----(119x,121x)
4 ------(131,133x) ----(137,139) -----(149,151)
5p ----(161x,163) ----(167,169x) ----(179,181)

6 ------(191,193) ------(197,199) -----(209x,211)
7p ----(221x,223) -----(227,229) ----(239,241)
8 ------(251,253x) -----(257,259x) ---(269,271)
9 ------(281,283) ------(287x,289x) --(299x,301x)
10 ----(311,313) ------(317,319x) ----(329x,331)

11p --(341x,343x) ---(347,349) -----(359,361x)
12 ----(371x,373) -----(377x,379) ---(389,391x)
13p --(401,403x) -----(407x,409) ---(419,421)
14 ----(431,433) -------(437x,439) ---(449,451x)
15 ----(461,463) -------(467,469x) ---(479,481x)

16 ----(491,493x) ------(497x,499) --(509,511x)
17p --(521,523) -------(527x,529x) -(539x,541)
18 ----(551x,553x) ----(557,559x) ---(569,571)
19 p -(581x,583x) -----(587,589x) --(599,601)
20 ----(611x,613) ------(617,619) ----(627x,631)

Milton L. Brown

[Non-text portions of this message have been removed]
• ... Isn t that the same thing as saying that they are either 11 & 13, or 17 & 19, or 29 & 31 mod 30?
Message 2 of 6 , Jun 8, 2005
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At 06:04 PM 6/8/2005, Milton Brown wrote:
>All twin primes after (29,31) are built as 30*k + (11,13) or +(17,19) or
>+(29,31)

Isn't that the same thing as saying that they are either 11 & 13, or 17 &
19, or 29 & 31 mod 30?
• Yes, obviously. And, you point is?
Message 3 of 6 , Jun 8, 2005
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Yes, obviously.

And, you point is?

> [Original Message]
> From: Jud McCranie <j.mccranie@...>
> To: <miltbrown@...>
> Date: 6/8/2005 7:29:38 PM
> Subject: Re: [PrimeNumbers] Building Twin Primes II
>
> At 06:04 PM 6/8/2005, Milton Brown wrote:
> >All twin primes after (29,31) are built as 30*k + (11,13) or +(17,19) or
> >+(29,31)
>
> Isn't that the same thing as saying that they are either 11 & 13, or 17 &
> 19, or 29 & 31 mod 30?
>
>
>
>
>
>
> Unsubscribe by an email to: primenumbers-unsubscribe@yahoogroups.com
> The Prime Pages : http://www.primepages.org/
>
>
>
>
>
>
>
• You ve only tested for 8 prime values below, a lot more are needed before we can make assertions. Andrew ... +(17,19) or +(29,31)
Message 4 of 6 , Jun 8, 2005
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You've only tested for 8 prime values below, a lot more are needed before
we can make assertions.

Andrew
--- In primenumbers@yahoogroups.com, "Milton Brown" <miltbrown@e...>
wrote:
> All twin primes after (29,31) are built as 30*k + (11,13) or
+(17,19) or +(29,31)
>
> Attached is a table for k from 1 to 20 showing their construction.
>
> The assertion is that for every k which is prime, there is at least one
> of the 3 additions which produces a twin prime.
>
> (30)k +(11,13) -------+(17,19) ------+(29,31)
> =================================
> 1 -------(41,31) --------(47,49x)------- (59,61)
> 2p -----(71,73) --------(77x,79) -------(89,91x)
> 3p ----(101,103) -----(107,109) -----(119x,121x)
> 4 ------(131,133x) ----(137,139) -----(149,151)
> 5p ----(161x,163) ----(167,169x) ----(179,181)
>
> 6 ------(191,193) ------(197,199) -----(209x,211)
> 7p ----(221x,223) -----(227,229) ----(239,241)
> 8 ------(251,253x) -----(257,259x) ---(269,271)
> 9 ------(281,283) ------(287x,289x) --(299x,301x)
> 10 ----(311,313) ------(317,319x) ----(329x,331)
>
> 11p --(341x,343x) ---(347,349) -----(359,361x)
> 12 ----(371x,373) -----(377x,379) ---(389,391x)
> 13p --(401,403x) -----(407x,409) ---(419,421)
> 14 ----(431,433) -------(437x,439) ---(449,451x)
> 15 ----(461,463) -------(467,469x) ---(479,481x)
>
> 16 ----(491,493x) ------(497x,499) --(509,511x)
> 17p --(521,523) -------(527x,529x) -(539x,541)
> 18 ----(551x,553x) ----(557,559x) ---(569,571)
> 19 p -(581x,583x) -----(587,589x) --(599,601)
> 20 ----(611x,613) ------(617,619) ----(627x,631)
>
>
> Milton L. Brown
>
> [Non-text portions of this message have been removed]
• ... My point is - what is your point? Your observation says nothing new.
Message 5 of 6 , Jun 8, 2005
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At 01:07 AM 6/9/2005, Milton Brown wrote:
>Yes, obviously.
>
>And, you point is?

My point is - what is your point? Your observation says nothing new.
• ... Well, the first counterexample is k=23, (701,703) (707,709) (719,721) The next few counterexamples are 31, 37, 41, 61, 73, 83, 97.
Message 6 of 6 , Jun 8, 2005
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At 06:04 PM 6/8/2005, Milton Brown wrote:
>All twin primes after (29,31) are built as 30*k + (11,13) or +(17,19) or
>+(29,31)
>
>Attached is a table for k from 1 to 20 showing their construction.
>
>The assertion is that for every k which is prime, there is at least one
>of the 3 additions which produces a twin prime.

Well, the first counterexample is k=23,
(701,703)
(707,709)
(719,721)

The next few counterexamples are 31, 37, 41, 61, 73, 83, 97.
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