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

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