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Re: [PrimeNumbers] Re: Brocard's Conjecture, and other notes

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  • 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 1 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 2 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 3 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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