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

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 Guest
Re: Prime Generalization Conjecture
Posted: Jun 20, 2009 11:01 AM

Oh I see you're not answering...(Revised)

Musatov wrote:
> On Jun 20, 4:06 am, Musatov <marty.musa...@gmail.com> wrote:
> > On Jun 20, 12:13 am, William Elliot <ma...@rdrop.remove.com> wrote:
> >

> > > On Fri, 19 Jun 2009, MeAmI.org wrote:
> > > > RULE: EVERY PRIME number is exactly
> > > >              1/2 of some other number +1.

> >
> > > So what?  For all x, x = (2x - 2)/2 + 1.
> >
> > > Trivial rule.
> > > Every integer (rational number, real number, complex number) is half
> > > of some integer (resp. rational number, real number, complex number)
> > > plus one.

> >
> > > Exercise.  How many primes are half of some prime plus one?

None. Half of a prime number is not a whole number. (Except 2, in
which case the whole number is 1).
17/2=8.5+1=9.5 (NP).

So we have the result:

RULE: No prime number greater than two is 1/2 another prime number
plus one.

But perhaps this is what you meant.

Inverse/Additive prime property per Musatov: (below)

RULE: EVERY PRIME number greater than 2 is twice a number +1.
3=1*2+1
5=2*2+1
7=3*2+1
11=5*2+1
13=6*2+1
17=8*2+1
19=9*2+1
23=11*2+1
29=14*2+1
31=15*2+1
37=18*2+1
41=20*2+1
43=21*2+1
47=23*2+1
51=25*2+1
53=26*2+1

And combined Prime Generalization: (Musatov)

RULE: Every prime greater than two is 1/2 a number +1 and twice a
number +1.

Now consider the series again, but this time plot the additive
difference between first and next doubled number.

In the first two terms we write....
3=1*2+1 #
5=2*2+1 1 because the difference between the doubled numbers from
first to the next was "1".

And we continue....
(here is the full table)
3=1*2+1 #
5=2*2+1 1
7=3*2+1 1
11=5*2+1 2
13=6*2+1 1
17=8*2+1 2
19=9*2+1 1
23=11*2+1 2
29=14*2+1 3
31=15*2+1 1
37=18*2+1 3
41=20*2+1 2
43=21*2+1 1
47=23*2+1 2
51=25*2+1 2
53=26*2+1 1

I would like to see if these reveals more to clarity to the set of
primes.

How might it?
Ben Bacarisse wrote:
> Musatov <marty.musatov@gmail.com> writes:
> > On Jun 20, 12:13 am, William Elliot <ma...@rdrop.remove.com> wrote:
> <snip>
> >> Exercise.  How many primes are half of some prime plus one?
> >
> > None. Half of a prime number is not a whole number.

>
> Except for 2.
>

> > So we have the result:
> >
> > RULE: No prime number is 1/2 another prime number plus one. (Except for )

>
> Just one prime number is exactly one plus 1/2 another prime number.

Oh yeah, which one?

> Copout per Ben.: Wording changed to avoid the ambiguity between p/2 + 1 and (p + 1)/2.)
++
Martin

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
6/26/09 Guest
6/26/09 Richard Heathfield
6/27/09 Guest
6/27/09 Guest
6/27/09 Guest
6/29/09 Peter Nilsson
6/30/09 Guest
6/30/09 Alf P. Steinbach
6/30/09 Richard Heathfield
6/30/09 Guest
6/30/09 Dik T. Winter
6/30/09 Richard Heathfield
6/30/09 Guest
6/30/09 Richard Heathfield
6/30/09 mike
6/30/09 Richard Heathfield
6/30/09 Guest
9/13/13
9/13/13
7/7/09 Constructive Truth
7/8/09 Alan Morgan
9/13/13
7/8/09 Guest
7/8/09 Guest
7/8/09 mike
7/8/09 Constructive Truth
7/8/09 Constructive Truth
7/12/09 mike
7/13/09 Guest
7/15/09 Guest
8/24/09 Guest
8/24/09 Guest
6/30/09 Guest
6/30/09 Ed Prochak
11/7/17 4musatov@gmail.com
6/20/09 William Elliot
6/20/09 Guest
6/20/09 Guest
6/20/09 Guest
6/20/09 Guest
6/20/09 Guest
2/8/14
9/13/13