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Re: [PrimeNumbers] Re: primes in arithmetic sequences

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  • Sam Shahrokhi
    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.
    Message 1 of 6 , Feb 27, 2009
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      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

















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    • Kermit Rose
      2. primes in arithmetic sequences Posted by: Sebastian Martin Ruiz s_m_ruiz@yahoo.es s_m_ruiz Date: Thu Feb 26, 2009 11:15 am ((PST)) Let p and q odd prime
      Message 2 of 6 , Feb 27, 2009
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        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
      • Maximilian Hasler
        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 3 of 6 , Feb 27, 2009
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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 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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          > [Non-text portions of this message have been removed]
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