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

 Messages: [ Previous | Next ]
 mike Posts: 34 Registered: 10/29/08
Re: Musatov Prime Generalization Conjecture
Posted: Jul 12, 2009 10:59 PM

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
> >
> >
> >

> > > 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

Date Subject Author
6/20/09 MeAmI.org
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