Hi Bryan,

Interesting twin prime sieve.

Using Pari in XP Pro,

primorial(n) = local(p1, x); if(n==0||n==1,return(1));p1=1;

forprime(x=2,n,p1*=x);return(p1)

g1(x) = primorial(x+1)

g2(x)=primorial(precprime(precprime(x)-1))

g(n)=g1(n)/g2(n)-(n^2-1)

ploth(k=1,200,g(k))

To see some detail

ploth(k=1,7,g(k))

You can also do

for(j=2,200,print(g(j)))

Then Open Excel first and in the dos box, highlight copy and paste

into excel to plot it there. If you don't open Excel first the clip board

will be cleared by Excel start up. Just another MS pain unless of course

there is a configuration option to disable this.

Also Your Dos box properties must be in quick edit and insert mode for

mouse highlight and right click to work. Also, layout screen buffer should be

at least the number of lines you print.

What is that curve?

Enjoy,

Cino Hilliard

To:

primenumbers@yahoogroups.com
From:

valareos@...
Date: Wed, 25 Mar 2009 08:55:03 +1000

Subject: [PrimeNumbers] Twin Conjecture visited

Disclaimer: I am a self taught amature mathematician. Information

that is here that may have been already found is in no way me claiming

responsibility for anothers work. Feel free to comment, or correct

mistakes.. it is how i learn

Let k be a number such that k-1 and k+1 are prime numbers (thus making

k+1 and k-1 twin primes)

the product of twin primes therefore will also always follow the format k^2-1

Assume that k+1 is the nth prime, and k-1 is the n-1th prime.

(k+1)# = p(1) * p(2) * p(3) * ... * p(n-2) * p(n-1) * p(n)

since k-1 is the n-1th prime,

(k-2)# = p(1) * p(2) * p(3) * ... * p(n-2)

thus, (k+1)#/(k-2)# = p(n-1) * p(n)

the products of twin primes can then also can be written as k+1# / k-2#

therefore,

(k+1)#/(k-2)# = k^2-1 for the twin primes (k-1), (k+1)

this can be placed in a formula y=[(x+1)# / (x-2)#] -(x^2-1)

If graphed, where the curve intercepts the x axis, it is the center

mark of a twin prime

From here, im looking to someone who can assist me in graphing this.

I can manually enter the points, but i dont have a graphing program

that can understand the Primorial expression #

Also curious if this can be extended further to prove that as k

approaches infinity, there are an infinite number of solutions where

(k+1)#/(k-2)# = k^2-1

--

Bryan Bartlett

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