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Topic: Prime Generalization Conjecture
Replies: 48   Last Post: Nov 7, 2017 5:14 PM

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 Guest
Re: Musatov Prime Generalization Conjecture
Posted: Jul 13, 2009 2:07 AM

On Jul 12, 7:59 pm, mike <m....@irl.cri.replacethiswithnz> wrote:
> In article <00e96645-4c61-491b-8a79-2a1ae4d3cf60
>
>
>

> > On Jul 8, 7:01 pm, mike <m....@irl.cri.replacethiswithnz> wrote:
> > > In article <88f7a7fc-702c-47ac-8f3e-66088faf4487
> > > @z4g2000prh.googlegroups.com>, marty.musa...@gmail.com says...

>
> > > >  Here are a list of statements, I would like to know if we can
> > > > properly
> > > >  decide from 2 N + 1:

>
> > > >  (All of the below statements assume P > 2, as you asserted.)
>
> > > >  Can we say....? (If every prime > 2 is 2 N + 1 = odd)
>
> > > >           1. 2 N + 1 = P an (odd) prime 1/2 (of an even) 2P?
>
> > > I assume that you trying to state:
>
> > > For all primes P of the form P = 2*N + 1, the number 2*P is even.
>
> > > If so then it is trivially true by definition.
>
> > > >            2. Can we then write for every prime > 2:
>
> > > >                 2 N + 1 = P (odd) and 2P (Even), N is also always
> > > > even?

>
> > > Here you appear to be stating:
> > > For all P > 2, P = 4*N + 1, for some natural number N.

>
> > > If so then this is trivially false as it doesn't hold true for 7.
>
> > > >            3. Can the above statement equivocally be stated:
>
> > > >             2 (even N) + 1 = Every Prime > 2 = 1/2 2P or 1/2 * 4 (even
> > > > N) + 2?

>
> > > >              2 * 8 + 1 = 17 (a prime) = 1/2 (17*2) or 1/2 * (4 * 8) +
> > > > 2 ?

>
> > > This seems teh same as 2 above. If so then it is false.
>
> > > Marty, it may interest you to note that as well as:
>
> > > For all P > 2, P = 2*N + 1
>
> > > being true, it is also the case that:
>
> > > For all P > 3, P = 6*N +/- 1
>
> > > -- Mike
>
> > This is very interesting. Thanks Mike. So we have all primes > 2 may
> > be written as 2 N + 1 or 6 N + / - 1. Can these equations be combined
> > to deduce something further?

>
> Oh yes, there are lots more patterns! How about:
> For all P > 5, P = 30*N +/- {1,7,11,13}
>
> ...with the obvious interpretation of the {} brackets.
>
> Mike- Hide quoted text -
>
> - Show quoted text -

Neat, huh?

Date Subject Author
6/20/09 MeAmI.org
6/20/09 Richard Heathfield
6/20/09 CBFalconer
6/21/09 Richard Heathfield
6/26/09 MeAmI.org
6/26/09 John H. Guillory
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6/30/09 Alf P. Steinbach
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