Re: [PrimeNumbers] Re: primes in arithmetic sequences

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• 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
Message 1 of 6 , Feb 27, 2009
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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