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Re: Brocard's Conjecture, and other notes

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  • Patrick Capelle
    ... Hello Jeremy, At the beginning of your proof of Brocard s conjecture,you wrote : Well if d-b = k, and a = b and c = d, then surely c-a = k . Surely
    Message 1 of 5 , Oct 7, 2005
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      --- In primenumbers@yahoogroups.com, Jeremy <mickleness@y...> wrote:
      >
      > Hi everyone... I just joined the list.
      >
      > I wrote a little paper on primes recently, offering an informal proof
      > of Brocard's Conjecture. a few notes on twin primes. and other
      > observations.
      >
      > I was wondering if people on this list could look it over and let me
      > know... well... if it has any merit. I'm competent at math, but
      > proofs and high level math are a little foreign to me...
      >
      > http://homepage.mac.com/bricolage1/essays/
      >


      Hello Jeremy,

      At the beginning of your proof of Brocard's conjecture,you wrote :
      "Well if d-b >= k, and a >= b and c >= d, then surely c-a >= k ".
      Surely not.There are cases where c-a < k.
      Take for instance a = 5, b = 2, c = 7, d = 6 and k = 3.

      Regards,
      Patrick Capelle.
    • Jeremy Wood
      Thanks. Hmmm... yeah I was suspect of that one. Back to square one. It still seems like the earlier expression involving pi((p(i+1)^2) really should lend
      Message 2 of 5 , Oct 7, 2005
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        Thanks. Hmmm... yeah I was suspect of that one.

        Back to square one. It still seems like the earlier
        expression involving pi((p(i+1)^2) really should lend
        itself to an insight into brocard's conjecture.

        - Jeremy Wood

        --- Patrick Capelle <patrick.capelle@...> wrote:

        > --- In primenumbers@yahoogroups.com, Jeremy
        > <mickleness@y...> wrote:
        > >
        > > Hi everyone... I just joined the list.
        > >
        > > I wrote a little paper on primes recently,
        > offering an informal proof
        > > of Brocard's Conjecture. a few notes on twin
        > primes. and other
        > > observations.
        > >
        > > I was wondering if people on this list could look
        > it over and let me
        > > know... well... if it has any merit. I'm
        > competent at math, but
        > > proofs and high level math are a little foreign to
        > me...
        > >
        > > http://homepage.mac.com/bricolage1/essays/
        > >
        >
        >
        > Hello Jeremy,
        >
        > At the beginning of your proof of Brocard's
        > conjecture,you wrote :
        > "Well if d-b >= k, and a >= b and c >= d, then
        > surely c-a >= k ".
        > Surely not.There are cases where c-a < k.
        > Take for instance a = 5, b = 2, c = 7, d = 6 and k =
        > 3.
        >
        > Regards,
        > Patrick Capelle.
        >
        >
        >
        >
      • Jeremy Wood
        After work I ll revisit everything again. In the meantime I kept the file online, but put red notes around the incorrect section. But the paper still points
        Message 3 of 5 , Oct 7, 2005
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          After work I'll revisit everything again. In the
          meantime I kept the file online, but put red notes
          around the incorrect section.

          But the paper still points out -- although it doesn't
          formally prove -- that:
          pi(p(i+1)^2)>=r(i)*(p(i+1)^2)+i-1
          where r(i) =
          (p(1)-1)/p(1)*(p(2)-1)/p(2)*...(p(i)-1)/p(i)

          If anyone has any thoughts as to how one could apply
          this towards Brocard's Conjecture, please let me know.
          Or if this is also flawed, please let me know.

          Cheers
          - Jeremy Wood

          --- Patrick Capelle <patrick.capelle@...> wrote:

          > --- In primenumbers@yahoogroups.com, Jeremy
          > <mickleness@y...> wrote:
          > >
          > > Hi everyone... I just joined the list.
          > >
          > > I wrote a little paper on primes recently,
          > offering an informal proof
          > > of Brocard's Conjecture. a few notes on twin
          > primes. and other
          > > observations.
          > >
          > > I was wondering if people on this list could look
          > it over and let me
          > > know... well... if it has any merit. I'm
          > competent at math, but
          > > proofs and high level math are a little foreign to
          > me...
          > >
          > > http://homepage.mac.com/bricolage1/essays/
          > >
          >
          >
          > Hello Jeremy,
          >
          > At the beginning of your proof of Brocard's
          > conjecture,you wrote :
          > "Well if d-b >= k, and a >= b and c >= d, then
          > surely c-a >= k ".
          > Surely not.There are cases where c-a < k.
          > Take for instance a = 5, b = 2, c = 7, d = 6 and k =
          > 3.
          >
          > Regards,
          > Patrick Capelle.
          >
          >
          >
          >
        • Jeremy Wood
          Sigh. Nevermind... taking the link down. The other expression is also flawed... it fails badly when i exceeds 35 (that is, (p(i))^2=22201). Back to the
          Message 4 of 5 , Oct 7, 2005
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            Sigh. Nevermind... taking the link down.

            The other expression is also flawed... it fails badly
            when i exceeds 35 (that is, (p(i))^2=22201).

            Back to the drawing board...

            --- Jeremy Wood <mickleness@...> wrote:

            > After work I'll revisit everything again. In the
            > meantime I kept the file online, but put red notes
            > around the incorrect section.
            >
            > But the paper still points out -- although it
            > doesn't
            > formally prove -- that:
            > pi(p(i+1)^2)>=r(i)*(p(i+1)^2)+i-1
            > where r(i) =
            > (p(1)-1)/p(1)*(p(2)-1)/p(2)*...(p(i)-1)/p(i)
            >
            > If anyone has any thoughts as to how one could apply
            > this towards Brocard's Conjecture, please let me
            > know.
            > Or if this is also flawed, please let me know.
            >
            > Cheers
            > - Jeremy Wood
            >
            > --- Patrick Capelle <patrick.capelle@...>
            > wrote:
            >
            > > --- In primenumbers@yahoogroups.com, Jeremy
            > > <mickleness@y...> wrote:
            > > >
            > > > Hi everyone... I just joined the list.
            > > >
            > > > I wrote a little paper on primes recently,
            > > offering an informal proof
            > > > of Brocard's Conjecture. a few notes on twin
            > > primes. and other
            > > > observations.
            > > >
            > > > I was wondering if people on this list could
            > look
            > > it over and let me
            > > > know... well... if it has any merit. I'm
            > > competent at math, but
            > > > proofs and high level math are a little foreign
            > to
            > > me...
            > > >
            > > > http://homepage.mac.com/bricolage1/essays/
            > > >
            > >
            > >
            > > Hello Jeremy,
            > >
            > > At the beginning of your proof of Brocard's
            > > conjecture,you wrote :
            > > "Well if d-b >= k, and a >= b and c >= d, then
            > > surely c-a >= k ".
            > > Surely not.There are cases where c-a < k.
            > > Take for instance a = 5, b = 2, c = 7, d = 6 and k
            > =
            > > 3.
            > >
            > > Regards,
            > > Patrick Capelle.
            > >
            > >
            > >
            > >
            >
            >
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