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23067Re: [PrimeNumbers] Re: Infinite Primes in an Arithmethic Progression

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  • Mathieu Therrien
    Sep 2, 2011
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      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
      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:


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