- Wouldn't this imply the twin prime conjecture ?

(for p=q+2 it would imply existence of another twin prime pair at

(q,p)+2t, and then so on)

Regards,

Maximilian

--- In primenumbers@yahoogroups.com, Sebastian Martin Ruiz

<s_m_ruiz@...> wrote:>

t2 positives integersï¿½that ï¿½p+t1(p-q) and q+t2(p-q) are primes.Can

> Hello:

> Let p and q odd prime numbers p>q by Dirichletï¿½theorem exist t1 and

someone prove that they exist by the same t?It is to sayï¿½exists a

positive integer t that p+t(p-q) and q+t(p-q) are both primes?> Sincerely

> Sebastian Martin Ruiz - Twin prime conjecture is precisely what I am trying to prove with this conjecture. We can prove by Dirichlet Theorem that exist the same t?We know by Dirichlet Theorem that exists infinity many t1 y t2 that p+t1(p-q) and q+t2(p-q) are both primes. But there are no two be equal?

--- El vie, 27/2/09, michael_b_porter <michael.porter@...> escribió:

De: michael_b_porter <michael.porter@...>

Asunto: Re: primes in arithmetic sequences

Para: "Sebastian Martin Ruiz" <s_m_ruiz@...>

Fecha: viernes, 27 febrero, 2009 6:02

--- In primenumbers@yahoogroups.com, Sebastian Martin Ruiz

<s_m_ruiz@...> wrote:> It is to say exists a positive integer t that p+t(p-q) and q+t(p-q)

are both primes?

Suppose that this conjecture is true. Let (s,s+2) be a pair of twin

primes. Then by the conjecture (with p=s+2, q=s), there is a positive

integer t such that s+2+2t and s+2t are both prime. So for each pair

of twin primes, there is a greater pair of twin primes.

So the twin prime conjecture follows from your conjecture.

- Michael Porter

[Non-text portions of this message have been removed] - Dear Sebastian:

In a recent work J.M. Deshouillers and F. Luca [On the distribution of some means concerning the densitiy, Funct. Approx. Comment. Math. Volume 39, Number 2 (2008), 335-344.] consider certain means of the values of the Euler function to prove that they are dense modulo one. At the Czech-Slovak Number Theory Conference in August 2007, F. Luca raised the question whether certain other sequences of mean values of the Euler function are uniformly distributed modulo one. Among these are the sequences of arithmetic and geometric means. Recently, J.M. Deshouillers and H. Iwaniec gave a method leading to an affirmative answer for Luca's question in the case of arithmetic mean, and a conditional answer for the case of geometric mean. The aim is to be framiliar with this method. it might be useful on your approach to prove twin prime number conjecture. meanwhile you can keep up yourself in connection with Professor Iwaniec.

Sincerely Yours.

Saeed Ranjbar

[Non-text portions of this message have been removed] - 2. primes in arithmetic sequences

Posted by: "Sebastian Martin Ruiz" s_m_ruiz@... s_m_ruiz

Date: Thu Feb 26, 2009 11:15 am ((PST))

Let p and q odd prime numbers p>q by Dirichlet theorem exist t1 and t2

positives integers that p+t1(p-q) and q+t2(p-q) are primes.Can someone

prove that they exist by the same t?It is to say exists a positive

integer t that p+t(p-q) and q+t(p-q) are both primes?

Sincerely

Sebastian Martin Ruiz

r1 = p+t1(p-q)

r2 = q+t2(p-q)

r1 - r2 = ( p+t1(p-q) ) - ( q+t2(p-q) )

r1 - r2 = (p - q) + t1 (p-q) - t2(p-q)

r1 - r2 = (1 + t1 - t2 ) (p - q)

If t1 = t2,

r1 - r2 = p - q

The existence of r1 and r2 is implied by the conjecture that

every even integer is the difference of two primes.

Kermit - Yes, there are common values for t1 y t2, but no-one can prove it yet.

I don't expect that this more general statement could be proved prior

to proving the twin prime conjecture (which is the special case p-q=2

where the values of t1, t2 are most dense - in fact you have a t1 and

a t2 for each prime larger than p resp. q).

Maximilian

On Fri, Feb 27, 2009 at 3:58 AM, Sebastian Martin Ruiz

<s_m_ruiz@...> wrote:>

> Twin prime conjecture is precisely what I am trying to prove with this conjecture. We can prove by Dirichlet Theorem that exist the same t?We know by Dirichlet Theorem that exists infinity many t1 y t2 that p+t1(p-q) and q+t2(p-q) are both primes. But there are no two be equal?

>

> --- El vie, 27/2/09, michael_b_porter <michael.porter@...> escribió:

>

> De: michael_b_porter <michael.porter@...>

> Asunto: Re: primes in arithmetic sequences

> Para: "Sebastian Martin Ruiz" <s_m_ruiz@...>

> Fecha: viernes, 27 febrero, 2009 6:02

>

> --- In primenumbers@yahoogroups.com, Sebastian Martin Ruiz

> <s_m_ruiz@...> wrote:

>> It is to say exists a positive integer t that p+t(p-q) and q+t(p-q)

> are both primes?

>

> Suppose that this conjecture is true. Let (s,s+2) be a pair of twin

> primes. Then by the conjecture (with p=s+2, q=s), there is a positive

> integer t such that s+2+2t and s+2t are both prime. So for each pair

> of twin primes, there is a greater pair of twin primes.

>

> So the twin prime conjecture follows from your conjecture.

>

> - Michael Porter

>

>

>

>

>

>

>

>

>

>

> [Non-text portions of this message have been removed]

>

>

>

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