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## 17059Re: [PrimeNumbers] Re: Brocard's Conjecture, and other notes

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• 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.
>
>
>
>
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