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Infinite Primes in an Arithmethic Progression

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  • Bob Gilson
    Could anyone explain, in simplistic terms, were that possible, how Legendre(?) proved that primes appearing in an arithmetic progression, continue to appear,
    Message 1 of 4 , Sep 1, 2011
      Could anyone explain, in simplistic terms, were that possible, how Legendre(?) proved that primes appearing in an arithmetic progression, continue to appear, with no limit.

      Alas I cannot find the proof on-line, and I doubt I would understand it, so a Terence Tao like explanation, would really be welcomed.

      Thanks

      Bob

      Sent from Samsung tablet
    • djbroadhurst
      ... Dirichlet s proof is here: http://tinyurl.com/3ef2l4o David
      Message 2 of 4 , Sep 1, 2011
        --- In primenumbers@yahoogroups.com,
        Bob Gilson <bobgillson@...> wrote:

        > Alas I cannot find the proof on-line

        Dirichlet's proof is here:

        http://tinyurl.com/3ef2l4o

        David
      • djbroadhurst
        ... For a modern account, in English, see http://www.math.uga.edu/~pete/4400DT.pdf where Pete Clark remarks: One of the amazing things about the proof of
        Message 3 of 4 , Sep 1, 2011
          --- In primenumbers@yahoogroups.com,
          "djbroadhurst" <d.broadhurst@...> wrote:

          > Dirichlet's proof is here:
          > http://tinyurl.com/3ef2l4o

          For a modern account, in English, see
          http://www.math.uga.edu/~pete/4400DT.pdf
          where Pete Clark remarks:

          "One of the amazing things about the proof of Dirichlet's theorem
          is how modern it feels. It is literally amazing to compare the
          scope of the proof to the arguments we used to prove some of the
          other theorems in the course, which historically came much later.
          ...
          Let us be honest that the proof of Dirichlet's theorem is of
          a difficulty beyond that of anything else we have attempted in
          this course."

          I remark that Selberg's "elementary proof" is also rather
          difficult. It is elementary only in the sense that
          he does not use complex characters or infinite sums:
          http://www.jstor.org/pss/1969454

          David
        • Mathieu Therrien
          This proof is awesome!!! Way too complicated for what it applies, but way too rich for the limits it implies! ________________________________ From:
          Message 4 of 4 , Sep 2, 2011
            This proof is awesome!!!

            Way too complicated for what it applies, but way too rich for the limits it implies!



            ________________________________
            From: djbroadhurst <d.broadhurst@...>
            To: primenumbers@yahoogroups.com
            Sent: Thursday, September 1, 2011 7:46:15 PM
            Subject: [PrimeNumbers] Re: Infinite Primes in an Arithmethic Progression


             


            --- In primenumbers@yahoogroups.com,
            "djbroadhurst" <d.broadhurst@...> wrote:

            > Dirichlet's proof is here:
            > http://tinyurl.com/3ef2l4o

            For a modern account, in English, see
            http://www.math.uga.edu/~pete/4400DT.pdf
            where Pete Clark remarks:

            "One of the amazing things about the proof of Dirichlet's theorem
            is how modern it feels. It is literally amazing to compare the
            scope of the proof to the arguments we used to prove some of the
            other theorems in the course, which historically came much later.
            ...
            Let us be honest that the proof of Dirichlet's theorem is of
            a difficulty beyond that of anything else we have attempted in
            this course."

            I remark that Selberg's "elementary proof" is also rather
            difficult. It is elementary only in the sense that
            he does not use complex characters or infinite sums:
            http://www.jstor.org/pss/1969454

            David




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