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Brocard's Conjecture, and other notes

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  • Jeremy
    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
    Message 1 of 5 , Oct 6, 2005
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      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/


      - Jeremy Wood

      P.S. Every time I proofread it I find at least one new typo... if
      you notice any typos, or want to discuss a particular part at length,
      please email me directly so we don't clutter up the list.
    • 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 2 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 3 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 4 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 5 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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