RULE: EVERY PRIME number is exactly
              1/2 of some other number +1.

MeAmI.org said:

> RULE: EVERY PRIME number is exactly
>               1/2 of some other number +1.

2 is a counter-example unless "other number" can mean "same number".

In general, if P = X / 2 + 1, then X = (P - 1) * 2, so your claim is 
tantamount to saying that for each prime number there exists some 
other number that can be reached by subtracting one from the prime 
number and then doubling the result. This leads us to some other 
observations of equal interest:

RULE: EVERY PERFECT SQUARE is exactly 1/2 of some other number +1.
RULE: EVERY PERFECT CUBE is exactly 1/2 of some other number +1.
RULE: EVERY FIBONACCI NUMBER is exactly 1/2 of some other number +1.
RULE: EVERY LUCAS NUMBER is exactly 1/2 of some other number +1.
RULE: EVERY INTEGER is exactly 1/2 of some other number +1.

Good solid stuff, but I don't think it's going to win a Fields Medal 
any time soon.

-- 
Richard Heathfield <http://www.cpax.org.uk>
Email: -http://www. +rjh@
Forged article? See 
http://www.cpax.org.uk/prg/usenet/comp.lang.c/msgauth.php
"Usenet is a strange place" - dmr 29 July 1999

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?

On Jun 20, 12:13=A0am, William Elliot <ma...@rdrop.remove.com> wrote:
> On Fri, 19 Jun 2009, MeAmI.org wrote:
> > RULE: EVERY PRIME number is exactly
> > =A0 =A0 =A0 =A0 =A0 =A0 =A01/2 of some other number +1.
>
> So what? =A0For all x, x =3D (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. =A0How many primes are half of some prime plus one?

Prime Generalization (by Musatov): EVERY PRIME number is exactly
               1/2 of a number +1.

Variant: RULE(0): EVERY PRIME number greater than two is exactly
              1/2 of some other number +1.

Prime Generalization (by Musatov): EVERY PRIME number is exactly
               1/2 of a number +1.

Variant: RULE(0): EVERY PRIME number greater than two is exactly
              1/2 of some other number +1.

On Jun 20, 12:13=A0am, William Elliot <ma...@rdrop.remove.com> wrote:
> On Fri, 19 Jun 2009, MeAmI.org wrote:
> > RULE: EVERY PRIME number is exactly
> > =A0 =A0 =A0 =A0 =A0 =A0 =A01/2 of some other number +1.
>
> So what? =A0For all x, x =3D (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. =A0How many primes are half of some prime plus one?

None. Half of a prime number is not a whole number.

17/2=3D8.5+1=3D9.5 (NP).

So we have the result:

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

On Jun 20, 4:06=A0am, Musatov <marty.musa...@gmail.com> wrote:
> On Jun 20, 12:13=A0am, William Elliot <ma...@rdrop.remove.com> wrote:
>
> > On Fri, 19 Jun 2009, MeAmI.org wrote:
> > > RULE: EVERY PRIME number is exactly
> > > =A0 =A0 =A0 =A0 =A0 =A0 =A01/2 of some other number +1.
>
> > So what? =A0For all x, x =3D (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. =A0How many primes are half of some prime plus one?
>
> None. Half of a prime number is not a whole number.
>
> 17/2=3D8.5+1=3D9.5 (NP).
>
> So we have the result:
>
> RULE: No prime number 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 is twice
              a number +1.
3=3D1*2+1
5=3D2*2+1
7=3D3*2+1
11=3D5*2+1
13=3D6*2+1
17=3D8*2+1
19=3D9*2+1
23=3D11*2+1
29=3D14*2+1
31=3D15*2+1
37=3D18*2+1
41=3D20*2+1
43=3D21*2+1
47=3D23*2+1
51=3D25*2+1
53=3D26*2+1

And combined Prime Generalization: (Musatov)

RULE: Every prime is 1/2 a number +1 and twice a number plus +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=3D1*2+1   #
5=3D2*2+1   1 because the difference between the doubled numbers from
the first to the next was "1".

And we continue....

(here is the full table)
3=3D1*2+1      #
5=3D2*2+1      1
7=3D3*2+1      1
11=3D5*2+1    2
13=3D6*2+1    1
17=3D8*2+1    2
19=3D9*2+1    1
23=3D11*2+1  2
29=3D14*2+1  3
31=3D15*2+1  1
37=3D18*2+1  3
41=3D20*2+1  2
43=3D21*2+1  1
47=3D23*2+1  2
51=3D25*2+1  2
53=3D26*2+1  1

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

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.

<snip>
> So we have the result:
>
> RULE: No prime number is 1/2 another prime number plus one.

Just one prime number is exactly one plus 1/2 another prime number.
(Wording changed to avoid the ambiguity between p/2 + 1 and (p + 1)/2.)

-- 
Ben.

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



Musatov wrote:
> On Jun 20, 4:06=A0am, Musatov <marty.musa...@gmail.com> wrote:
> > On Jun 20, 12:13=A0am, William Elliot <ma...@rdrop.remove.com> wrote:
> >
> > > On Fri, 19 Jun 2009, MeAmI.org wrote:
> > > > RULE: EVERY PRIME number is exactly
> > > > =A0 =A0 =A0 =A0 =A0 =A0 =A01/2 of some other number +1.
> >
> > > So what? =A0For all x, x =3D (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. =A0How 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=3D8.5+1=3D9.5 (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=3D1*2+1
5=3D2*2+1
7=3D3*2+1
11=3D5*2+1
13=3D6*2+1
17=3D8*2+1
19=3D9*2+1
23=3D11*2+1
29=3D14*2+1
31=3D15*2+1
37=3D18*2+1
41=3D20*2+1
43=3D21*2+1
47=3D23*2+1
51=3D25*2+1
53=3D26*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=3D1*2+1   #
5=3D2*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=3D1*2+1      #
5=3D2*2+1      1
7=3D3*2+1      1
11=3D5*2+1    2
13=3D6*2+1    1
17=3D8*2+1    2
19=3D9*2+1    1
23=3D11*2+1  2
29=3D14*2+1  3
31=3D15*2+1  1
37=3D18*2+1  3
41=3D20*2+1  2
43=3D21*2+1  1
47=3D23*2+1  2
51=3D25*2+1  2
53=3D26*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=A0am, William Elliot <ma...@rdrop.remove.com> wrote:
> <snip>
> >> Exercise. =A0How 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 a=
nd (p + 1)/2.)
++
Martin

Richard Heathfield wrote:
> MeAmI.org said:
> 
>> RULE: EVERY PRIME number is exactly
>>               1/2 of some other number +1.
> 
> 2 is a counter-example unless "other number" can mean "same number".

Oh? 3 is 'another number'. 3+1 = 4 (usually).  4/2 = 2 (usually).

-- 
 [mail]: Chuck F (cbfalconer at maineline dot net) 
 [page]: <http://cbfalconer.home.att.net>
            Try the download section.

CBFalconer said:

> Richard Heathfield wrote:
>> MeAmI.org said:
>> 
>>> RULE: EVERY PRIME number is exactly
>>>               1/2 of some other number +1.
>> 
>> 2 is a counter-example unless "other number" can mean "same
>> number".
> 
> Oh? 3 is 'another number'. 3+1 = 4 (usually).  4/2 = 2 (usually).

Division has precedence over addition. Even if it didn't, 
associativity would be left to right unless specified otherwise.

Let "some other number" be X.

(X / 2) + 1 = 2

Subtract one from both sides.

X / 2 = 2 - 1

X / 2 = 1

X = 2

QED

-- 
Richard Heathfield <http://www.cpax.org.uk>
Email: -http://www. +rjh@
Forged article? See 
http://www.cpax.org.uk/prg/usenet/comp.lang.c/msgauth.php
"Usenet is a strange place" - dmr 29 July 1999

Martin Musatov: (as MeAmI.org wrote)

Richard Heathfield wrote:
> CBFalconer said:
>
> > Richard Heathfield wrote:
> >> MeAmI.org said:
> >>
> >>> RULE: EVERY PRIME number is exactly
> >>>               1/2 of some other number +1.
> >>
> >> 2 is a counter-example unless "other number" can mean "same
> >> number".
> >
> > Oh? 3 is 'another number'. 3+1 = 4 (usually).  4/2 = 2 (usually).
>
> Division has precedence over addition. Even if it didn't,
> associativity would be left to right unless specified otherwise.
>
> Let "some other number" be X.
>
> (X / 2) + 1 = 2
>
> Subtract one from both sides.
>
> X / 2 = 2 - 1
>
> X / 2 = 1
>
> X = 2
>
> QED
>
> --
> Richard Heathfield <http://www.cpax.org.uk>
> Email: -http://www. +rjh@
> Forged article? See
> http://www.cpax.org.uk/prg/usenet/comp.lang.c/msgauth.php
> "Usenet is a strange place" - dmr 29 July 1999

Thank you.

--
Musatov

On Fri, 26 Jun 2009 03:15:23 -0700 (PDT), "MeAmI.org"
<MeAmI@vzw.blackberry.net> wrote:

>Martin Musatov: (as MeAmI.org wrote)
>
>Richard Heathfield wrote:
>> CBFalconer said:
>>
>> > Richard Heathfield wrote:
>> >> MeAmI.org said:
>> >>
>> >>> RULE: EVERY PRIME number is exactly
>> >>>               1/2 of some other number +1.
I suppose given 

                 1/2 of 2 = 1  
                                   1 + 1 = 2  

Does this take into account eg.    4.5/2 =  2.25
  So would that make 3.25 a prime number?  

On Jun 26, 1:20=A0pm, John H. Guillory <jo...@communicomm.com> wrote:
> On Fri, 26 Jun 2009 03:15:23 -0700 (PDT), "MeAmI.org"
>
> <Me...@vzw.blackberry.net> wrote:
> >Martin Musatov: (as MeAmI.org wrote)
>
> >Richard Heathfield wrote:
> >> CBFalconer said:
>
> >> > Richard Heathfield wrote:
> >> >> MeAmI.org said:
>
> >> >>> RULE: EVERY PRIME number is exactly
> >> >>> =A0 =A0 =A0 =A0 =A0 =A0 =A0 1/2 of some other number +1.
>
> I suppose given
>
> =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A01/2 of 2 =3D 1 =A0
> =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A01 =
+ 1 =3D 2 =A0
>
> Does this take into account eg. =A0 =A04.5/2 =3D =A02.25
> =A0 So would that make 3.25 a prime number? =A0

A decimal number is not by classical definition prime. Though if you
have an idea of a decimal equivalent of primality, I would love to
hear it.

--

Musatov

"Tear a whole in Cyberspace"
http://MeAmI.org

Search for Truth!

Musatov said:

> On Jun 26, 1:20 pm, John H. Guillory <jo...@communicomm.com>
> wrote:
<snip>
>> So would that make 3.25 a prime number?
> 
> A decimal number is not by classical definition prime.

Numbers aren't decimal. They're numbers. Decimal is a system for 
/representing/ numbers textually.


> Though if
> you have an idea of a decimal equivalent of primality, I would
> love to hear it.

It's a meaningless concept. Primality has nothing to do with 
representation.

-- 
Richard Heathfield <http://www.cpax.org.uk>
Email: -http://www. +rjh@
Forged article? See 
http://www.cpax.org.uk/prg/usenet/comp.lang.c/msgauth.php
"Usenet is a strange place" - dmr 29 July 1999

Musatov wrote:
Richard Heathfield wrote:
> Musatov said:
>
> > On Jun 26, 1:20 pm, John H. Guillory <jo...@communicomm.com>
> > wrote:
> <snip>
> >> So would that make 3.25 a prime number?
> >
> > A decimal number is not by classical definition prime.
>
> Numbers aren't decimal. They're numbers. Decimal is a system for
> /representing/ numbers textually.
>
>
> > Though if
> > you have an idea of a decimal equivalent of primality, I would
> > love to hear it.
>
> It's a meaningless concept. Primality has nothing to do with
> representation.
>
> --
> Richard Heathfield <http://www.cpax.org.uk>
> Email: -http://www. +rjh@
> Forged article? See
> http://www.cpax.org.uk/prg/usenet/comp.lang.c/msgauth.php
> "Usenet is a strange place" - dmr 29 July 1999

Dear Mr. Heathfield,

I agree with you in the classical proof sense primality is as much
governed by physics as it is counting numbers we choose to represent
quantities.

My intention with this reference is providing a means to interface
between prime numbers to the left of the decimal point and decimal
numbers to the right of the decimal point. Perhaps a system where 3.17
refers to two primes, and this sense I am speaking mostly toward
computation, but again I assert, numbers to the left or right of the
decimal, are still just numbers.

I have always been fascinated by this notion:

Numerically, our representations do not appear uniform instinctually,
to me at least.

Here is an example.

If we say, "What 10 is to 20 is not what 2.2 is to 3.3," is there any
truth in proportion to justify this assertion in physics or
mathematics?

We are simply counting.

10 is to 20
....is...
20 is 2x 10

2.2 is to 3.3
....is...
3.3 is 1.5x 2.2
....or...
1/2 of 2.2+2.2=3.3
....or...
1/2 of 2.2=1.1*3=3.33

1 and 1/2 of 2.2=3.3
      ...or...
   1.5 of 2.2=3.3

So there is a split of

1/2+2/5+3/5=15/10
..5+.4+.6=1.5

....And...

1/2*2/5*3/5=x
x=5/10*4/10*6/10=120/10=1.2

..5*.4*.6=1.2

Theorem: use of a set of given quantities.

Rule: adding the set produces at least the product.

Proof(1a): 1 apple + 2 apples + 3 apples=6 apples.

Proof(1b):1 apple * 2 apples * 3 apples=6 apples.

Proof(2a): 5 apples + 4 apples + 6 apples =16 apples.

Proof(2b): 5 apples * 4 apples * 6 apples=120 apples.

Contradiction: in the above example the sum=1.5 and the product=1.2.

Fallacy: Multiplying quantities of items does not shrink them. This
applies to measurements and transforms.

But as we count from 1 to 2 and then 2 to 3

10/1.1 = 9.0909091
20/2.2 = 9.0909091
30/3.3 = 9.0909091

What 1
....is to...
10
....is...
What 2.2 is 22

Proof:  1.1/10=.11
          2.2/20=.1
         2.2/22=.11

Martin Musatov

Musatov worte:
Musatov wrote:
> Musatov wrote:
> Richard Heathfield wrote:
> > Musatov said:
> >
> > > On Jun 26, 1:20 pm, John H. Guillory <jo...@communicomm.com>
> > > wrote:
> > <snip>
> > >> So would that make 3.25 a prime number?
> > >
> > > A decimal number is not by classical definition prime.
> >
> > Numbers aren't decimal. They're numbers. Decimal is a system for
> > /representing/ numbers textually.
> >
> >
> > > Though if
> > > you have an idea of a decimal equivalent of primality, I would
> > > love to hear it.
> >
> > It's a meaningless concept. Primality has nothing to do with
> > representation.
> >
> > --
> > Richard Heathfield <http://www.cpax.org.uk>
> > Email: -http://www. +rjh@
> > Forged article? See
> > http://www.cpax.org.uk/prg/usenet/comp.lang.c/msgauth.php
> > "Usenet is a strange place" - dmr 29 July 1999
>
> Dear Mr. Heathfield,
>
> I agree with you in the classical proof sense primality is as much
> governed by physics as it is counting numbers we choose to represent
> quantities.
>
> My intention with this reference is providing a means to interface
> between prime numbers to the left of the decimal point and decimal
> numbers to the right of the decimal point. Perhaps a system where 3.17
> refers to two primes, and this sense I am speaking mostly toward
> computation, but again I assert, numbers to the left or right of the
> decimal, are still just numbers.
>
> I have always been fascinated by this notion:
>
> Numerically, our representations do not appear uniform instinctually,
> to me at least.
>
> Here is an example.
>
> If we say, "What 10 is to 20 is not what 2.2 is to 3.3," is there any
> truth in proportion to justify this assertion in physics or
> mathematics?
>
> We are simply counting.
>
> 10 is to 20
> ...is...
> 20 is 2x 10
>
> 2.2 is to 3.3
> ...is...
> 3.3 is 1.5x 2.2
> ...or...
> 1/2 of 2.2+2.2=3.3
> ...or...
> 1/2 of 2.2=1.1*3=3.33
>
> 1 and 1/2 of 2.2=3.3
>       ...or...
>    1.5 of 2.2=3.3
>
> So there is a split of
>
> 1/2+2/5+3/5=15/10
> .5+.4+.6=1.5
>
> ...And...
>
> 1/2*2/5*3/5=x
> x=5/10*4/10*6/10=120/10=1.2
>
> .5*.4*.6=1.2
>
> Theorem: use of a set of given quantities.
>
> Rule: adding the set produces at least the product.
>
> Proof(1a): 1 apple + 2 apples + 3 apples=6 apples.
>
> Proof(1b):1 apple * 2 apples * 3 apples=6 apples.
>
> Proof(2a): 5 apples + 4 apples + 6 apples =15 apples.
>
> Proof(2b): 5 apples * 4 apples * 6 apples=120 apples.
>
> Contradiction: in the above example the sum=1.5 and the product=1.2.
>
> Fallacy: Multiplying quantities of items does not shrink them. This
> applies to measurements and transforms.
>
> But as we count from 1 to 2 and then 2 to 3
>
> 10/1.1 = 9.0909091
> 20/2.2 = 9.0909091
> 30/3.3 = 9.0909091
>
> What 1
> ...is to...
> 10
> ...is...
> What 2.2 is 22
>
> Proof:  1.1/10=.11
>           2.2/20=.1
>          2.2/22=.11
>
> Martin Musatov

Musatov wrote:
Musatov wrote:
Musatov wrote:
Musatov wrote: Richard Heathfield wrote:
Musatov said:
 On Jun 26, 1:20 pm, John H. Guillory <jo...@communicomm.com>
wrote:
<snip>
 So would that make 3.25 a prime number? A decimal number is not by
classical definition prime.
Numbers aren't decimal. They're numbers. Decimal is a system for
/representing/ numbers textually.

Though if
you have an idea of a decimal equivalent of primality, I would
love to hear it.

It's a meaningless concept. Primality has nothing to do with
representation.
Richard Heathfield <http://www.cpax.org.uk> Email: -http://www. +rjh@
Forged article? See
http://www.cpax.org.uk/prg/usenet/comp.lang.c/msgauth.php
"Usenet is a strange place" - dmr 29 July 1999
Dear Mr. Heathfield,
I agree with you in the classical proof sense primality is as much
governed by physics as it is counting numbers we choose to represent
quantities.

My intention with this reference is providing a means to interface
between prime numbers to the left of the decimal point and decimal
numbers to the right of the decimal point. Perhaps a system where 3.17
refers to two primes, and this sense I am speaking mostly toward
computation, but again I assert, numbers to the left or right of the
decimal, are still just numbers.

I have always been fascinated by this notion:

Numerically, our representations do not appear uniform instinctually,
to me at least.

Here is an example.
If we say, "What 10 is to 20 is not what 2.2 is to 3.3," is there any
truth in proportion to justify this assertion in physics or
mathematics?

We are simply counting.

10 is to 20
 ...is...
 20 is 2x 10
 2.2 is to 3.3
 ...is...
3.3 is 1.5x 2.2
....or...
1/2 of 2.2+2.2=3.3
....or...
1/2 of 2.2=1.1*3=3.33

1 and 1/2 of 2.2=3.3
      ...or...
   1.5 of 2.2=3.3
So there is a split of

1/2+2/5+3/5=15/10
..5+.4+.6=1.5

....And...

 1/2*2/5*3/5=x
 x=5/10*4/10*6/10=120/10=1.2

..5*.4*.6=1.2

Theorem: use of a set of given quantities.

Rule: adding the set produces at least the product.

Proof(1a): 1 apple + 2 apples + 3 apples=6 apples.

Proof(1b):1 apple * 2 apples * 3 apples=6 apples.

Proof(2a): 5 apples + 4 apples + 6 apples =15 apples.

Proof(2b): 5 apples * 4 apples * 6 apples=120 apples.

Contradiction: in the above example the sum=1.5 and the product=1.2.

Fallacy: Multiplying quantities of items does not shrink them. This
applies to measurements and transforms.

 But as we count from 1 to 2 and then 2 to 3

 10/1.1 = 9.0909091
 20/2.2 = 9.0909091
 30/3.3 = 9.0909091

 What 1
 ...is to...
 10
 ...is...
 What 2.2 is 22

 Proof:  1.1/10=.11
           2.2/20=.1
          2.2/22=.11
 Martin Musatov

Richard Heathfield <r...@see.sig.invalid> wrote:
> CBFalconer said:
> > Richard Heathfield wrote:
> > > MeAmI.org said:
> > > > RULE: EVERY PRIME number is exactly
> > > >               1/2 of some other number +1.

Every prime is exactly half of +1?!

> > >
> > > 2 is a counter-example unless "other number" can mean "same
> > > number".
> >
> > Oh? 3 is 'another number'. 3+1 = 4 (usually).  4/2 = 2 (usually).
>
> Division has precedence over addition. Even if it didn't,
> associativity would be left to right unless specified otherwise.

If I have 4 dollars and 20 cents, what is half the dollars and cents?

  a) $1.20
  b) $2.10
  c) $2.20
  d) $2.40

--
Peter

Martin Musatov wrote:
Peter Nilsson wrote:
> Richard Heathfield <r...@see.sig.invalid> wrote:
> > CBFalconer said:
> > > Richard Heathfield wrote:
> > > > MeAmI.org said:
> > > > > RULE: EVERY PRIME number is exactly
> > > > >               1/2 of some other number +1.
>
> Every prime is exactly half of +1?!
>
> > > >
> > > > 2 is a counter-example unless "other number" can mean "same
> > > > number".
> > >
> > > Oh? 3 is 'another number'. 3+1 = 4 (usually).  4/2 = 2 (usually).
> >
> > Division has precedence over addition. Even if it didn't,
> > associativity would be left to right unless specified otherwise.
>
> If I have 4 dollars and 20 cents, what is half the dollars and cents?
>
>   a) $1.20
>   b) $2.10
>   c) $2.20
>   d) $2.40
>
> --
> Peter

Dear Peter,

Thank you for your reply. Before I respond to your question, please
allow me a brief moment to clarify my conjecture:

"Musatov's Prime Generalization Conjecture": Every prime greater than
2 is 2n+1=P.

2*1+1=3
2*2+1=5
....
2*20+1=41
....

(1)Is my conjecture provable?

Okay, thanks for your patience.

Peter, the answer to the question is "b)2.10".

But please bear with me and consider the following scenario:

Suppose I have three quantities of loose coins:

1) $0.50
2) $0.40
3) $0.60

The sum of the three quantities is $1.50.

Now suppose we are multiplying those same three quantities of coins:

$0.50*$0.40*$0.60

..50*.40=.20

And...

..20*.60=$0.12.

(2)Why should multiplying our money result in a loss of $1.38 or a 92%
loss?

If the three sums were dollars the case would be different.

$50+$40+$60=$150
$50*$40+$60=$1200

I do understand how to solve the problem literally, but chose to show
this example to prove decimal representations fail basic rationale.

++
Musatov

* Musatov:
> 
> "Musatov's Prime Generalization Conjecture": Every prime greater than
> 2 is 2n+1=P.
> 
> 2*1+1=3
> 2*2+1=5
> ...
> 2*20+1=41
> ...
> 
> (1)Is my conjecture provable?

Yes but it's completely silly to conjecture that primes greater than 2 are odd.


Cheers & hth.,

- Alf

-- 
Due to hosting requirements I need visits to <url: http://alfps.izfree.com/>.
No ads, and there is some C++ stuff! :-) Just going there is good. Linking
to it is even better! Thanks in advance!

Peter Nilsson said:

> Richard Heathfield <r...@see.sig.invalid> wrote:
<snip>
>>
>> Division has precedence over addition. Even if it didn't,
>> associativity would be left to right unless specified otherwise.
> 
> If I have 4 dollars and 20 cents, what is half the dollars and
> cents?
> 
>   a) $1.20
>   b) $2.10
>   c) $2.20
>   d) $2.40

None of the above. Observe:

#include <stdio.h>
#include <iso646.h>

int half(int x)
{
  return x / 2;
}

int main(void)
{
  int dollars = 4;
  int cents = 20;
  int answer = half(dollars) and cents;
  printf("The answer is %d\n", answer);
  return 0;
}

Output:

The answer is 1


-- 
Richard Heathfield <http://www.cpax.org.uk>
Email: -http://www. +rjh@
Forged article? See 
http://www.cpax.org.uk/prg/usenet/comp.lang.c/msgauth.php
"Usenet is a strange place" - dmr 29 July 1999

*Musatov:
Alf P. Steinbach wrote:
> * Musatov:
> >
> > "Musatov's Prime Generalization Conjecture": Every prime greater than
> > 2 is 2n+1=P.
> >
> > 2*1+1=3
> > 2*2+1=5
> > ...
> > 2*20+1=41
> > ...
> >
> > (1)Is my conjecture provable?
>
> Yes but it's completely silly to conjecture that primes greater than 2 are odd.
>
>
> Cheers & hth.,
>
> - Alf
>
> --
> Due to hosting requirements I need visits to <url: http://alfps.izfree.com/>.
> No ads, and there is some C++ stuff! :-) Just going there is good. Linking
> to it is even better! Thanks in advance!

Dear Alf,

Thanks for the reply.  I figure I have to start somewhere, thanks for
bearing with me.

(1)So have we established every  prime greater than 2 is 2N+1?

(2)Also, "2N+1"="odd", correct?

To quote (play on) the movie "Pi":

Musatov: "11:31pm. Restate my assumptions".

1. Every prime is odd.

2. "2N+1" is every prime greater than 2.

3. "2N+1" is every odd.

4. 2N+1 contains every prime greater than 2 plus every odd composite.

5. All prime factors of odd composites are contained in "2N+1".

6. The set of prime numbers and prime factors of of odd composites is
wholly contained in the set "2N+1".

........Breather........

The next step is then to establish the case when "N" is even, in every
case "2N+1" is odd. If all of "2N+1" is odd then this is a given.

Now we further examine the states:

When "N" ends in "2":

2*2=4+1=5 is prime, but only the first time. Every number ending in 5
greater than 5 is composite.

So to generate primes by this method we can rule out all numbers
ending in "2".

Then,

N of all even numbers we can say, there only remains numbers ending in
"4, 6, and 8".

Consider each case:

For four: (#4)

2*4+1=9 not prime
2*14+1=29 prime
2*24+1=49 not prime

In the above instances "N" ends in "4" and is not prime, the formula
produces a number with square prime factors (i.e. 3*3=9 and 7*7=49).
(i.e. When it does not produce a prime the composite is a prime
squared).

Also, we note:

When "N" ends in "4" and the formula produces a composite number,
adding "two" to the composite produces a prime.

Shown:
2*4+1=9+2=11 prime
2*24+1=49+2=51 prime

Moving along...

For Six: (i.e. When "N" ends in "6" and is applied 2N+1)

2*6=12+1=13 prime
2*16=32+1=33 is not prime.
2*26=52+1=53 prime

As above when "N" ends in 6 and does not produce prime (as above) we
have two prime factors.

In the above case of 33 they are "3 and 11". Of those two prime
factors, adding 2 to each produces 2 more primes. Shown:

3+2=5 prime
11+2=13 prime

Now, onto 8:
2*8+1=17 prime
2*18+1=37 prime
2*28+1=57 prime
2*38+1=77 not prime

In the above we have when "N" ends in "8" and does not produce a prime
as applied (2N+1) it has produced a number with two prime factors:

77=11*7

11 and 7 are prime.

Also, 11+2 is prime.

However, 7+4 is prime.

The conjecture contains:

"Musatov Prime Generalization Conjecture": "Every prime number and
prime factors of odd composites, is contained in the set 2N+1."

The natural further question is how and when do prime factors appear
in even composites and what rules apply?

So we have separated the primes and prime factors of odd composites
into a set (2N+1), now the only remaining prime factors exist inside
even composites and outside of this set.

A lot to chew on, but I thank you all in advance and look forward to
the insight gained from your responses.

Signed,

++
Musatov

Musatov wrote:
Alf P. Steinbach wrote:
> * Musatov:
> >
> > "Musatov's Prime Generalization Conjecture": Every prime greater than
> > 2 is 2n+1=P.
> >
> > 2*1+1=3
> > 2*2+1=5
> > ...
> > 2*20+1=41
> > ...
> >
> > (1)Is my conjecture provable?
>
> Yes but it's completely silly to conjecture that primes greater than 2 are odd.
>
>
> Cheers & hth.,
>
> - Alf
>
> --
> Due to hosting requirements I need visits to <url: http://alfps.izfree.com/>.
> No ads, and there is some C++ stuff! :-) Just going there is good. Linking
> to it is even better! Thanks in advance!


What is "hth"?

++
Musatov

On Jun 30, 1:12=A0am, Musatov <marty.musa...@gmail.com> wrote:
> Martin Musatov wrote:
> Peter Nilsson wrote:
> > Richard Heathfield <r...@see.sig.invalid> wrote:
> > > CBFalconer said:
> > > > Richard Heathfield wrote:
> > > > > MeAmI.org said:
> > > > > > RULE: EVERY PRIME number is exactly
> > > > > > =A0 =A0 =A0 =A0 =A0 =A0 =A0 1/2 of some other number +1.
>
> > Every prime is exactly half of +1?!
>
> > > > > 2 is a counter-example unless "other number" can mean "same
> > > > > number".
>
> > > > Oh? 3 is 'another number'. 3+1 =3D 4 (usually). =A04/2 =3D 2 (usual=
ly).
>
> > > Division has precedence over addition. Even if it didn't,
> > > associativity would be left to right unless specified otherwise.
>
> > If I have 4 dollars and 20 cents, what is half the dollars and cents?
>
> > =A0 a) $1.20
> > =A0 b) $2.10
> > =A0 c) $2.20
> > =A0 d) $2.40
>
> > --
> > Peter
>
> Dear Peter,
>
> Thank you for your reply. Before I respond to your question, please
> allow me a brief moment to clarify my conjecture:
>
> "Musatov's Prime Generalization Conjecture": Every prime greater than
> 2 is 2n+1=3DP.
>
> 2*1+1=3D3
> 2*2+1=3D5
> ...
> 2*20+1=3D41
> ...
>
> (1)Is my conjecture provable?
>
It is trivial in that ANY ODD NUMBER can be written as 2*n+1. Since
all primes beyond 2 are odd, this formula tells us nothing about
primes. Your conjecture is true but not yours.  It is common
knowledge.

  Ed