Prime Generalization Conjecture
MeAmI.org
1/2 of some other number +1.
Richard Heathfield
> 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
William Elliot
> 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?
Musatov
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
Musatov
1/2 of a number +1.
Variant: RULE(0): EVERY PRIME number greater than two is exactly
Martin Michael Musatov
> 1/2 of some other number +1.
>
>
>
>
>
2*4=8-1=7
4*6=24-1=23
6*8=48-1=47
8*10=80-1=79
10*12=120-1=119
12*14=168-1=167
14*16=224-1=223
16*18=288-1=287
18*20=360-1=259
20*22=440-1=439
22*24=528-1=527
24*26=624-1=623
26*28=728-1=727
28*30=840-1=839
30*32=960-1=959
32*34=1088-1=1087
34*36=1224-1=1223
36*38=1368-1=1367
The vertical columns read: 8, 4, 8, 0, 0 repeating
7, 3, 7, 9, 9 repeating
respectively
Inside product is always divisible by two to infinity.
MeAmI.org
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Martin Michael Musatov
Theorem: Beginning with 1 every number doubled then multiplied by half the number minus one is prime. (with exception of the 7th term, which is continuously divisible by 7. [and reducible to a prime].
Infinite Double Prime Generator - Generator
The first number is one.
Double one is two.
2*1-1=1
Double two is four.
4(2)=8-1=7
8(4)=32-1=31
16(8)=128-1=127
32(16)=512-1=511
Among the countable [set
the first doubled number is two.]
numbers the first two are the number
one and two. Beginning with two
double the number multiplied by
1/2 the number -1 is constantly
prime*.
*with exception every 7th term has factor 7, reducible to prime.
1st Term: 4(2)=8-1=7
2nd Term: 8(4)=32-1=31
3rd Term: 16(8)=128-1=127
4th Term: 32(16)=512-1=511
5th Term: 64(32)=2048-1=2047
6th Term: 128(64)=8192-1=8191
7th Term: 256(128)=32768-1=32767 (Composite: 7th term 32767/7=4681)
8th Term: 512(256)=131072-1=131071
References:
American Psychological Association (APA):
prime number. (n.d.). Dictionary.com Unabridged (v 1.1). Retrieved June 20, 2009, from Dictionary.com website: http://dictionary.reference.com/browse/prime number
Chicago Manual Style (CMS):
prime number. Dictionary.com. Dictionary.com Unabridged (v 1.1). Random House, Inc. http://dictionary.reference.com/browse/prime number (accessed: June 20, 2009).
Modern Language Association (MLA):
"prime number." Dictionary.com Unabridged (v 1.1). Random House, Inc. 20 Jun. 2009. <Dictionary.com http://dictionary.reference.com/browse/prime number>.
Institute of Electrical and Electronics Engineers (IEEE):
Dictionary.com, "prime number," in Dictionary.com Unabridged (v 1.1). Source location: Random House, Inc. http://dictionary.reference.com/browse/prime number. Available: http://dictionary.reference.com. Accessed: June 20, 2009.
BibTeX Bibliography Style (BibTeX)
@article {Dictionary.com2009,
title = {Dictionary.com Unabridged (v 1.1)},
month = {Jun},
day = {20},
year = {2009},
url = {http://dictionary.reference.com/browse/prime number},
}
Thank you,
Martin Musatov
Founder, MeAmI.org
"Google Google Googling, plus no ads!" Visit http://MeAmI.org.
Musatov
None. Half of a prime number is not a whole number.
17/2=8.5+1=9.5 (NP).
So we have the result:
RULE: No prime number is 1/2 another prime number plus one.
Musatov
But perhaps this is what you meant.
Inverse/Additive prime property per Musatov: (below)
RULE: EVERY PRIME number 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 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=1*2+1 #
5=2*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=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 series of
primes...
Ben Bacarisse
> On Jun 20, 12:13 am, William Elliot <ma...@rdrop.remove.com> wrote:
>> 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.
MeAmI.org
RULE: Every prime greater than three is twice a number plus one and half plus one.
Numerically, this is stated:
RULE: Every prime greater than 3 is 1/2X+1=P=2N+1.
..Or...
RULE: Every prime greater than 3 is 1/2 a number +1 and twice a number +1.
For example,
3=1/2(4)+1
3=2(1)+1
Martin Musatov
Founder, MeAmI.org
"Google Google Googling, plus no ads.
Visit http://MeAmI.org for more.
MeAmI.org
> > 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.
Please think before you snip.
You were wrong here.
> <Errant 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.
<Snip>
Which prime and what is the whole number?
Musatov
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....@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
CBFalconer
> 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.
Richard Heathfield
> 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
Bacle
> <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?
>
> Prime Generalization (by Musatov): EVERY PRIME number
> is exactly
> 1/2 of a number +1.
>
Prime Generalization: by anyone with a 1st grade
knowledge of basic algebra:
?
As William said,
1): 2=(2/2)+1
2) Odd primes are _by def._ of the form 2n+1.
Then 2n+1 =(4n/2)+1 .
You must have considered this conjecture for a
full 2 seconds, right?
And you didn't get that?. I can see how you are
careless in not thinking the conjecture thru, but
even after they explain it to you, you don't get it?
Bacle
> <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.
>
> 17/2=8.5+1=9.5 (NP).
(2/2)+1=2
So your whole NP fails, however unrelated it is
to primes.
>
> So we have the result:
>
> RULE: No prime number is 1/2 another prime number
> plus one.
2=(2/2)+1 .
Do you think for even a few seconds before posting?
MeAmI.org
> 1/2 of some other number +1.
>
>
>
>
>
Yes. Do you?
(1/2)2+1=2=P
(1/2)3+1=2.5=NP
2/2+1=2(P)
3/2+1=2.5(NP)
Bacle
Really?. 1/2 of _another_ number:
3=4/2 +1
5=8/2 +1
...
p=(2p-2)/2 +1 (*)
....
(*:W. Elliott mentioned this one before me, BTW)
Or do you think that 4,8 do not qualify as "other
numbers" ?. Do you think 2p-2 is not "another number"?
Just because 3 does not work does not invalidate the claim. Anyone with a 1st grade education would know that. Do you?. Or are you just too dishonest to
admit to a very basic mistake?.
If you are not in high school now, you have some
serious problems, not just with math, but with basic
English comprehension, if you cannot correctly
interpret the meaning of "another number".
Now, I understand you made the conjecture carelessly;
it happens. But you cannot understand why it's wrong?
Seriously?
And if you are throwing around big names like P
and NP, you might want to learn your (very) basics
beforehand, together with the fact that there is no immediate connection between the two issues at hand.
MeAmI.org
Thank you.
--
Musatov
Musatov
> 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
> >> >>> 1/2 of some other number +1.
>
>
> 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?
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!
Richard Heathfield
> 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.
Vincenzo Librandi
>>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)
See OEIS - A005097
Regards,
Vincenzo ibrandi
Musatov
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
Musatov worte:
Musatov
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.
Peter Nilsson
> 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
Musatov
Martin Musatov wrote:
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
Alf P. Steinbach
>
> "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!
KMF
I am not sure I know what you are asking, but this
seems to have a very trivial answer:
Every prime larger than 2 is necessarily odd. Every
odd number can be represented as 2n+1 . To get an
actual representation , just divide your odd number
O by 2, and take the reminder: 17=2*8+1, etc.
As W.Elliot said before, for p>2 a prime:
p=(2p-1)/2 + 1
>
> 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?
Your net result is not in $ , but in $^3 units.
You are getting something that is not strictly $
in this sense, so it does not seem to make sense
to compare the two.
This is like the comparison between length and
volume. If you have a box of lengths 0.4u, 0.5u, 0.6u
then the box has _volume_ .12u^3 , where u is any
unit of length, and u^3 is a unit of volume.
I don't see how you can find a meaningful way of
comparing length with volume.
>
> If the three sums were dollars the case would be
> different.
>
> $50+$40+$60=$150
> $50*$40+$60=$1200
>
Now all summands are expressed in the same unit $,
so it makes sense to add them.
> I do understand how to solve the problem literally,
> but chose to show
> this example to prove decimal representations fail
> basic rationale.
>
I don't think they do, if you consider the units
issue. If you do not, then multiplying by , e.g.,
1/2 can be seen as getting a half of an amount,
and it then makes sense to have it be smaller.
> ++
> Musatov
>
Fishcake
> 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?
Yes.
Proof: Suppose that P = 2n. If n > 1, then P is not a prime, since P is not equal to 2 and is divisible by 2.
--------------
Musatov, I have another conjecture JUST for you:
Every prime P other than 3 is either P = 3N + 1 or 3N + 2.
Can this be proved?
Everyone else, don't say anything.
--------------
Richard Heathfield
> 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
Musatov
*Musatov:
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
Fishcake wrote:
> >
> > 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?
>
> Yes.
>
> Proof: Suppose that P = 2n. If n > 1, then P is not a prime, since P is not equal to 2 and is divisible by 2.
>
> --------------
Signed,
Musatov
P.S. Dear Fishcake,
You have an interesting name. Why did you choose it? Also, thanks for
the opportunity to learn.
>
> Musatov, I have another conjecture JUST for you:
>
> Every prime P other than 3 is either P = 3N + 1 or 3N + 2.
>
> Can this be proved?
>
> Everyone else, don't say anything.
>
> --------------
Re: your question...
Hmmm... I only did a little bit of research on this one, so I am going
to have to go with my gut and say "Yes".
To the best of my understanding, every prime greater than "3" may be
written as "6N+1" or "6N-1". (In other words every prime other than
the primes 2 and 3). And since 6N+1 is the same thing as 3N+1 (but
with one more N) this seems to work. As for the 3N+2, this seems to me
to be the same as 6N-1 (with one less N) so this seems to work.
Is "Yes" the correct answer?
--
Musatov
Also...
Based on some search, here are some computation results I'd like to
share:
The 3n + 1 problem. ... 1. input n. 2. print n. 3. if n = 1 then
STOP ... sequence of numbers will be printed 22 11 34 17 52 26 13 40
20 10 5 16 8 4 2 1 ...
http://online-judge.uva.es/p/v1/100.html
Programming Challenges
The 3n + 1 problem ... If n is even, divide by 2. If n is odd,
multiply by 3 and add 1. ... 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2
1 ...
So the algorithm works! Right? Is the problem solved given the below
and the above?
Evaluate np if m=-2/3,n=1/2 and p=-3 3/4?
np means n times p does it not? Thus it becomes 1/2 times -3 3/4. Thus
1/2 times -15/4 becomes -15/8 ... = 1/2(- 3 3/4) = 1/2(- 15/4) = -
15/8 or - 1 7/8 ...
And if we could resolve P versus NP it would mean we'd be off to the
races to hopefully help some people...
3n.1 What vaccines are currently under development? ... 3, P. 118).
Information about efforts to produce an AIDS ... page up: Childhood
Vaccinations FAQ · next page: 3n.2 What other research is being done
to improve vaccines? ...
PII: S0305-0548(98)00080-XB), j"3n#1, 3n#2,2,4n, p. L> ". (0;B;B !B).
Claim. ¹here is a desired partition if and only if there is a schedule
whose makespan is no greater than ...
http://linkinghub.elsevier.com/retrieve/pii/S030505489800080X
3n 2n n 3n 3n 6n n n 1 2n 1 3n (1, l) (b, 2n) (3n, r) 1 ≤ l, r ...3n.
2. $'ˆ˜vgD–—mF“PzFnˆ{”‡‰ˆD's“Pˆc•—–™˜F $''dve5 f'‰k†m5•jdDk! .... 1 ≤
n ≤. 1 000 000 000, 1 ≤ l, r < 2n, 1 < b < 3n ... P. P. Q. Q turn 1
turn 2 ...
http://ioinformatics.org/locations/ioi05/contest/day0/pol/pol.pdf
++
Musatov
http://MeAmI.org
"Google rewrote their API shortly after we launched. We heard they
also called their mothers."
Musatov
Musatov wrote:
Dear Sci.Math,
As above it is written "_volume_" instead of "volume", why?
My guess is the _underscore_ does something to the data to separate it
or make it useful to users to integrate in a program of some sort. I
wonder what could in theory be done with information off Sci.Math as
to require such strange notation. This notation only seems to "pop up"
deep in sets or threads, but does so quite frequently surrounding
certain discussions surrounding "P vs. NP", such as here:
::::::::(1)What are all the practical reasons to write "_term_"
instead of just "term" where "term" is any word some Sci.Math users
write as "_term_"?
Thank you,
++
Musatov
Musatov
(sorry, forgot to past the link)
Musatov
Musatov
What is "hth"?
++
Musatov
Dik T. Winter
...
When are you going to stop to post these mindless conjectures based on a
very small number of cases?
> 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).
Wrong. 2*34+1 = 69 = 3*23.
2*544+1 = 1089 = 3*3*11*11
2*364+1 = 729 = 3*3*3*3*3*3
> 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
Since when is 51 prime?
--
dik t. winter, cwi, science park 123, 1098 xg amsterdam, nederland, +31205924131
home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/
Richard Heathfield
> In article
> <115c718c-fe66-4a34...@i6g2000yqj.googlegroups.com>
> Musatov <marty....@gmail.com> writes: ...
<snip>
> > Shown:
> > 2*4+1=9+2=11 prime
> > 2*24+1=49+2=51 prime
>
> Since when is 51 prime?
It's odd, right? And primes (ignoring 2, which is clearly
experimental error) are odd, right? Therefore, 51 is prime, QED.
Bacle
> Alf P. Steinbach wrote:
> > * Musatov:
> > >
> > > "Musatov's Prime Generalization Conjecture":
> Every prime greater than
> > > 2 is 2n+1=P.
I think it makes sense that you give your name to
something so absolutely trivial.
> > >
> > > 2*1+1=3
> > > 2*2+1=5
> > > ...
> > > 2*20+1=41
> > > ...
> > >
> > > (1)Is my conjecture provable?
> >
It is laughable that you described yourself as
a prodigy, and yet cannot figure out something any
fifth grader would know. You also chided me when
I questioned whether you know mathematics. This
post proves to me that you don't.
The fact that you have had this explained to you
many times, and that you keep going back to asking
the same question, and you keep posting over and over
the same trivially false conjectures, pretentiously called "musatov conjecture" even after you have been given many counterexamples, shows me you are a pretentious idiot, uninterested in learning anything.
Now, we are all ignorant at some point, but on top of that,you refuse to pay attention to corrections and comments, and keep posting thoughtless garbage.
We welcome those interested in learning. You are
definitely not one of them.
Please go post your garbage somewhere else, we
don't have many other sites for us, but there are
plenty of sites for feeble-minded lunatics like you.
Conjecture: every even number can be written
in the form 2n.
Musatov
> Dik T. Winter said:
>
> > In article
> > Musatov <marty.musa...@gmail.com> writes: ...
>
> <snip>
>
> > > Shown:
> > > 2*4+1=9+2=11 prime
> > > 2*24+1=49+2=51 prime
>
> > Since when is 51 prime?
>
> It's odd, right? And primes (ignoring 2, which is clearly
> experimental error) are odd, right? Therefore, 51 is prime, QED.
>
> --
> Richard Heathfield <http://www.cpax.org.uk>
> Email: -http://www. +rjh@
> "Usenet is a strange place" - dmr 29 July 1999
No. 3*17 = 51
So 51 has 4 factors: 1, 3, 17, and 51
Musatov
You are assuming. Assumptions are not always correct.
Musatov
I never described myself as a prodigy. I challenge any who say this
provide a reference.
It is careless to make claims without citations, especially when they
are damaging.
Musatov
Bacle
> I never described myself as a prodigy. I challenge
> any who say this
> provide a reference.
>
> It is careless to make claims without citations,
> especially when they
> are damaging.
>
> Musatov
http://mathforum.org/kb/thread.jspa?forumID=13&threadID=1943615&messageID=6730100#6730100
And you make these unfounded claims repeatedly,
trashing this site. This site has been going on
for a while, with its own idiosyncrasy, and yet you
come in and turn it into your personal playground
of self-veneration.
Bacle
you should go over the many proofs that have been made
that P=/NP and look for flaws in them.
And then stop posting 90% off-topic material here.
Then I really won't care what you choose to do after
that.
Bacle
you believe yourself to be a prodigy:
Your conjecture that every prime p>2 can be written
as p=2n+1 shows you lack the most basic understanding
of what a prime is. Nothing wrong with that itself.
But being so clearly ignorant of the topic and
throwing around conjectures really makes you look like
a conceited clown. Ask basic questions, read the replies carefully, absorb the material, _then_ make
well-informed conjectures. OWise, you throw around
unneccesary trivialities. Repeatedly. And , believe
it or not, this site is not your personal playground;
it is a site where people like me want to do serious
math, and we do not have many other places to do so.
And you are trashing this site.
Richard Heathfield
> On Jun 30, 6:21 am, Richard Heathfield <r...@see.sig.invalid>
> wrote:
>> Dik T. Winter said:
>>
>> > In article
>> >
<115c718c-fe66-4a34-ac7c-02b57c508...@i6g2000yqj.googlegroups.com>
>> > Musatov <marty.musa...@gmail.com> writes: ...
>>
>> <snip>
>>
>> > > Shown:
>> > > 2*4+1=9+2=11 prime
>> > > 2*24+1=49+2=51 prime
>>
>> > Since when is 51 prime?
>>
>> It's odd, right? And primes (ignoring 2, which is clearly
>> experimental error) are odd, right? Therefore, 51 is prime, QED.
>>
>
> No. 3*17 = 51
WHOOOOOOSH!!
mike
r...@see.sig.invalid says...
> Dik T. Winter said:
>
> > In article
> > <115c718c-fe66-4a34...@i6g2000yqj.googlegroups.com>
> > Musatov <marty....@gmail.com> writes: ...
>
> <snip>
>
> > > Shown:
> > > 2*4+1=9+2=11 prime
> > > 2*24+1=49+2=51 prime
> >
> > Since when is 51 prime?
>
> It's odd, right? And primes (ignoring 2, which is clearly
> experimental error) are odd, right? Therefore, 51 is prime, QED.
>
is prime.
Mike
Musatov
> In article <_9qdnbY6rMCzjdfXnZ2dnUVZ8tZi4...@bt.com>,
> r...@see.sig.invalid says...
>
>
>
> > Dik T. Winter said:
>
> > > In article
> > > Musatov <marty.musa...@gmail.com> writes: ...
>
> > <snip>
>
> > > > Shown:
> > > > 2*4+1=9+2=11 prime
> > > > 2*24+1=49+2=51 prime
>
> > > Since when is 51 prime?
>
> > It's odd, right? And primes (ignoring 2, which is clearly
> > experimental error) are odd, right? Therefore, 51 is prime, QED.
>
> Come now Richard, you have to ignore 3 and 17 as well to prove that 51
> is prime.
>
>
> - Show quoted text -
If it is known that if any NP-complete language is sparse (contains no
more than a polynomial number of strings of length n), then P = NP.
[BH08] improved this result, showing that if any language in NP has an
NP-hard set of subexponential density, then coNP is contained in NP/
poly and thus, by [Yap82], PH collapses to the third level.
Conceptually, a decision problem is a problem that takes as input some
string, and outputs "yes" or "no". If there is an algorithm (say a
Turing machine, or a computer program with unbounded memory) which is
able to produce the correct answer for any input string of length
Failed to parse (<math_output_error>): n
in at most c \cdot n^k steps, where k and Failed to parse
(<math_output_error>): c are constants independent of the input
string, then we say that the problem can be solved in polynomial time
and we place it in the class P. Formally, P is defined as the set of
all languages which can be decided by a deterministic polynomial-time
Turing machine. That is,
P = {L:L = L(M) for some deterministic polynomial-time Turing machine
M}
where L(M) = \{ w\in\Sigma^{*}: M \text{ accepts } w \}
and a deterministic polynomial-time Turing machine is a deterministic
Turing machine M which satisfies the following two conditions:
1. M halts on all input w; and
2. there exists k \in N such that T_{M}(n)\in\; O(nk),
where T_{M}(n) = \max\{ t_{M}(w) : w\in\Sigma^{*}, \left|w
\right| = n \}
and tM(w) = number of steps M takes to halt on input w.
NP can be defined similarly using nondeterministic Turing machines
(the traditional way). However, a modern approach to define NP is to
use the concept of certificate and verifier. Formally, NP is defined
as the set of languages over a finite alphabet that have a verifier
that runs in polynomial time, where the notion of "verifier" is
defined as follows.
Let Failed to parse (<math_output_error>): L
be a language over a finite alphabet, Σ.
L\in\mathbf{NP} if, and only if, there exists a binary relation R
\subset\Sigma^{*}\times\Sigma^{*} and a positive integer k such that
the following two conditions are satisfied:
1. For all x\in\Sigma^{*}, x\in L \Leftrightarrow\exists y\in\Sigma^
{*} such that (x,y)\in R\; and \left|y\right|\in\;O(\left|x\right|^
{k}); and
2. the language L_{R} = \{ x\# y:(x,y)\in R\} over \Sigma\cup\{\#\}
is decidable by a Turing machine in polynomial time.
A Turing machine that decides LR is called a verifier for L and a y
such that (x,y)\in R is called a certificate of membership of x in L.
In general, a verifier does not have to be polynomial-time. However,
for L to be in NP, there must be a verifier that runs in polynomial
time. --MartinMichaelMusatov 07:18, 24 February 2009 (UTC)
NPC: NP-Complete
The class of decision problems such that (1) they're in NP and (2)
every problem in NP is reducible to them (under some notion of
reduction). In other words, the hardest problems in NP.
Two notions of reduction from problem A to problem B are usually
considered:
1. Karp or many-one reductions. Here a polynomial-time algorithm is
given as input an instance of problem A, and must produce as output an
instance of problem B.
2. Turing reductions, in this context also called Cook reductions.
Here the algorithm for problem B can make arbitrarily many calls to an
oracle for problem A.
Some examples of NP-complete problems are discussed under the entry
for NP.
The classic reference on NPC is [GJ79].
Unless P = NP, NPC does not contain any sparse problems: that is,
problems such that the number of 'yes' instances of size n is upper-
bounded by a polynomial in n [Mah82].
A famous conjecture [BH77] asserts that all NP-complete problems are
polynomial-time isomorphic -- i.e. between any two problems, there is
a one-to-one and onto Karp reduction. If that's true, the NP-complete
problems could be interpreted as mere "relabelings" of one another.
NP-complete problems are p-superterse unless P = NP [BKS95]. This
means that, given k Boolean formulas F1,...,Fk, if you can rule out
even one of the 2k possibilities in polynomial time (e.g., "if
F1,...,Fk-1 are all unsatisfiable then Fk is satisfiable"), then P =
NP.
--
Musatov
Ed Prochak
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
Richard Heathfield
That would have been a different jest. Mine was more along the lines
of "all cats are animals, this dog is an animal, therefore this dog
is a cat".
Musatov
Regarding my prime generalization and my claim to resolution of [P
Versus NP] please add the below to consideration:
Suppose, for example, the interval in the arguments above between 0
and
1 and is partitioned to the following scheme:
0 < 1/2^n < 1/2^n-1 < [...] < 1/8 < 1/4 <1/2 <1.[in + finite tree]
Clearly the largest subinterval in the partition has width 1/2, and
its width remains 1/2 no matter how n is increased.
The function then necessarily produces prime numbers continually by
keeping N at 1/2.
I am now going to paste my proof P==NP to combine threads/logic:
> > > > > > > > > > > > Because you do not check the lines in order.
> > > > > > > > > > > > It is always your basic assumption that you
> > > > > > > > > > > > first check the first line and after that
> > > > > > > > > > > > the next line. That is wrong.
> > > > > > > > > > > That is necessary because you cannot find the n-th
> > > > > > > > > > > line unless you know the line number n - 1 or some
> > > > > > > > > > > equivalent mark.
> > ...
> > > > > > Why does it imply checking the previous lines? Why do you not
> > > > > > answer
> > > > > > that question?
> > > > > You cannot check line n without knowing line n-1.
> > > > But why does that imply *checking* line n-1? Why do you not answer that
> > > > question?
> > > It implies knowing line n-1. It implies counting till that number.
> > And still no answer to my question, and what you write here is wrong. In
> > the bijection of the rationals > 0 and the naturals I have so often shown,
> > to know the rational maped to 66 you need only know the rationals mapped
> > to lines 1, 2, 4, 8, 16, 32 and 33. So I need not to know the rational
> > mapped to 65.
> > But my question was: "why is knowing a line the same as checking a line"?
> > Because you originally asserted: "when checking line n of Cantor's list
> > you need to check all previous lines". What is that? Nonsense or not?
> Whether or not it is nonsense, it is irrelevant, since the Cantor
> argument applies to all lines simultaneoulsy with a single rule.
> --
> Virgil- Hide quoted text -
I vow to donate the entire $1MM to charity.
M.M. Musatov
MichaelW
here:
http://qwiki.stanford.edu/wiki/Complexity_Zoo:N
I have also detected text from the Wikipedia entry although you have
not bothered to clean up the failed pasting of the mathematic symbols.
http://en.wikipedia.org/wiki/P_%3D_NP_problem
Regards, MichaelW.
MeAmI.org
Pay close attention my post is different than the current complexity
zoo
Pay attention to math output error phrase
MeAmI.org
Pay close attention and compare the above to the current complexity
zoo page.
What differences exist?
MichaelW
You tell me. As far as I can see you have just grabbed text without
understanding the content. You even keep the internal references (e.g.
"GJ79") which only make sense in terms of the original site.
Regards, Michael W.
jillbones
Every integer is represented either 3N, 3N+1 or
3N+2. Need I go further?
Bill J
> --
> Musatov
>
> Also...
>
> Based on some search, here are some computation results I'd like to
> share:
>
> The 3n + 1 problem. ... 1. input n. 2. print n. 3. if n = 1 then
> STOP ... sequence of numbers will be printed 22 11 34 17 52 26 13 40
> 20 10 5 16 8 4 2 1 ...
>
> http://online-judge.uva.es/p/v1/100.html
>
> Programming Challenges
> The 3n + 1 problem ... If n is even, divide by 2. If n is odd,
> multiply by 3 and add 1. ... 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2
> 1 ...
>
> http://www.programming-challenges.com/pg.php%3Fpage%3Ddownloadproblem...
> - 9k -
>
> So the algorithm works! Right? Is the problem solved given the below
> and the above?
>
> Evaluate np if m=-2/3,n=1/2 and p=-3 3/4?
>
> np means n times p does it not? Thus it becomes 1/2 times -3 3/4. Thus
> 1/2 times -15/4 becomes -15/8 ... = 1/2(- 3 3/4) = 1/2(- 15/4) = -
> 15/8 or - 1 7/8 ...
>
> And if we could resolve P versus NP it would mean we'd be off to the
> races to hopefully help some people...
>
> 3n.1 What vaccines are currently under development? ... 3, P. 118).
> Information about efforts to produce an AIDS ... page up: Childhood
> Vaccinations FAQ · next page: 3n.2 What other research is being done
> to improve vaccines? ...
>
> http://stason.org/TULARC/child-parent/vaccinations/3n-1-What-vaccines...
MeAmI.org
Precisely, Michael W. understanding the content in the context it was
generated in is crucial to the proof.
Very good observation.
--
Musatov
MeAmI.org
{{x}}  L halts in Polynomial time.Let y  halts
in . ...http://www.docendi.org/re-t243853.html - 44k -
[ABOVE IS MARTIN MICHAEL MUSATOV'S P==NP PROOF TEXT POSED AS A ...
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Constructive Truth
> In article <115c718c-fe66-4a34-ac7c-02b57c508...@i6g2000yqj.googlegroups.com> Musatov <marty.musa...@gmail.com> writes:
> ...
> When are you going to stop to post these mindless conjectures based on a
> very small number of cases?
>
> > Consider each case:
> >
> > For four: (#4)
Dear Mr. Dik T. Winter:
I am afraid, necessarily you misunderstand the direct language of my
claim.
My claim is:
1. every prime is of the form 2N+1.
My claim is:
2. Not every number of the form 2N+1 is prime.
They are two very different things, but may be stated directly with
the statement I made earlier.
"Every prime number is of the form 2N+1"
Do you understand?
--
Martin Musatov
Venn Diagram/Concentric circle inclusions/statements may help me
clarify.
_____________________
[ All Numbers of the ]
[ {Prime Numbers} ]
[ form 2N+1 ]
----------------------
1. All prime numbers are of the form 2N+1
2. Not all numbers of the form 2N+1 are prime.
Alan Morgan
Constructive Truth <scri...@aol.com> wrote:
>I am afraid, necessarily you misunderstand the direct language of my
>claim.
>
>My claim is:
>
>1. every prime is of the form 2N+1.
Not only is your statement trivial and completely uninteresting (every
prime number is odd. Really? Could that be because even numbers are,
by definition, divisible by 2, and thus not prime?), it isn't even
completely correct. 2 is a prime, but is not of the form 2N+1.
So your claim is both trivial and false. Have no fear! One minor
change:
Musatov-Morgan Theorem
Every prime > 2 is of the form 2N+1
and it's now trivial and true. What's next? A variation on the
Goldbach Conjecture where you hypothesize that every number > 2
can be written as the sum of two other numbers?
Alan
--
Defendit numerus
Musatov
> In article <01ecf301-15ba-4bfb-83c3-f4e8e18c9...@o18g2000pra.googlegroups.com>,
> Constructive Truth <scribe...@aol.com> wrote:
>
> >I am afraid, necessarily you misunderstand the direct language of my
> >claim.
>
> >My claim is:
>
> >1. every prime is of the form 2N+1.
>
> Not only is your statement trivial and completely uninteresting (every
> prime number is odd. Really? Could that be because even numbers are,
> by definition, divisible by 2, and thus not prime?), it isn't even
> completely correct. 2 is a prime, but is not of the form 2N+1.
>
> So your claim is both trivial and false. Have no fear! One minor
> change:
>
> Musatov-Morgan Theorem
> Every prime > 2 is of the form 2N+1
>
> and it's now trivial and true. What's next? A variation on the
> Goldbach Conjecture where you hypothesize that every number > 2
> can be written as the sum of two other numbers?
>
> Alan
> --
> Defendit numerus
Hello Alan,
Thank you for your feedback and write up. Very cool!
Can you explain something to me please? By your comments, I
understand, 2 N + 1 = odd. But what else can we say about 2 N + 1 ?
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?
For example:
2*8+1=17
1/2*34=17
2. Can we then write for every prime > 2:
2 N + 1 = P (odd) and 2P (Even), N is also always even?
3. Can the above statement equivocally be stated:
2 (even N) + 1 = Every Prime = 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)?
Thank you for your time an patience.
> Musatov-Morgan Theorem
> Every prime > 2 is of the form 2N+1
So cool, thanks again!
Martin Musatov
Musatov
For example:
2*8+1=17
1/2*34=17
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 ?
Thank you for your time and patience.
Musatov-Morgan Theorem
Every prime > 2 is of the form 2N+1
So cool, thanks again! Good save.
Martin Musatov
I just caught a little mistake, fixed ity.
_...@jeff_relf.seattle.invalid
Are you the www.divinityDice.COM Michael Wallace, in Burringbar, NSW ?
If so, Double-A in Alt.Astronomy wants to know
where Bee-Ji(Harmonic12) posts these days.
Bee's most-recent post was June 23, 2006:
www.google.com/groups/search?q=&enc_author=YBcvZBoAAACGeyG_oqClQecrY0wwPc-chCtlwmSeL11StUiFEqj7pA&scoring=d
Last known post, June 23, 2006:
NightBat said:
“ it's the Team Glow shirts and caps
'cause women just can't resist them! ”.
Bee replied:
“ oH Yeah!? Where is my cap and shirt Sir! I have moved.
L Bee ”.
news:449cc0e6$0$27623$afc3...@news.optusnet.com.au
Both Bee and her mate, Michael Wallace(a.k.a. "Vital Aqua") used:
Harmonic12 @ optusNet.COM.AU
What's more, they both stopped posting at the same time.
Michael Wallace, Northern New South Wales, Australia, +07.3206.8606:
www.byronbum.com/Burringbar/images/burringbar_map_subdivision.pdf
www.byronbum.com/Burringbar/PAGES/Burringbar.htm
Lot One Upper Burringbar Road
Burringbar, NSW 2483
AU
phone&Fax: 61 2 66770080
One of his long-inActive webSites: www.Env-Board.COM
They make “PlasterBoard”, Drywall, 5 million Sq Meters per annum.
“ Send mail to info @ numberHarmonics.COM
with questions or comments about this web site.
Copyright © 2004 Env Board Australia
Last modified: August 27, 2004 ”
Telephone / Fax: (int) 61 7 32068606
PO Box 399 Burringbar NSW Australia 2483
His active “Ladder to the Moon Publications” site:
www.divinityDice.COM
Last modified: April 12, 2009
www.divinityDice.COM/dictionary.htm
info @ divinityDice.COM
mike
@z4g2000prh.googlegroups.com>, marty....@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
I.N.R.I. Logic
> In article <88f7a7fc-702c-47ac-8f3e-66088faf4487
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?
Can we write every prime not equal to 3 may be written as 3 N + / -
1 ?
Does
2 (even N) + 1 = Every Prime =/= 7 > 2 = 1/2 2P or 1/2 * 4
(even N) + 2?
Or does the single 7 present only an iceberg head in fatally flawed
logic?
I.N.R.I. Logic (aka, Martin Musatov -- for now)
I.N.R.I. Logic
>
> - Show quoted text -
I want you to pay close attention to the logic. I referred to "all
primes" meaning "all" not each. Therefore the statement is valid, do
you agree?
Though three cannot be written as 6n + or - 1 it can be written as 2N
+1 so the statement is true.
The statement would be false if I said "each prime" but I did not.
Kai-Uwe Bux
[...]
> 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?
No. Any number of the form 6N+1 and any number of the form 6N-1 is already
odd, i.e., of the form 2N+1.
> Can we write every prime not equal to 3 may be written as 3 N + / -
> 1 ?
Yes: any number that is not a multiple of 3 can be written as 3N+1 or 3N-1.
> Does
> 2 (even N) + 1 = Every Prime =/= 7 > 2 = 1/2 2P or 1/2 * 4
> (even N) + 2?
Huh?
> Or does the single 7 present only an iceberg head in fatally flawed
> logic?
If you are asking whether there are primes other than 7 of the form 4N+3,
then the answer is yes: e.g., 11, 19, 31, ...
In fact, there are infinitely many such primes.
Best
Kai-Uwe Bux
MeAmI.org
> I.N.R.I. Logic wrote:
>
> [...]
>
> > 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?
>
> No. Any number of the form 6N+1 and any number of the form 6N-1 is already
> odd, i.e., of the form 2N+1.
>
> > Can we write every prime not equal to 3 may be written as 3 N + / -
> > 1 ?
>
> Yes: any number that is not a multiple of 3 can be written as 3N+1 or 3N-1.
>
> > Does
> > 2 (even N) + 1 = Every Prime =/= 7 > 2 = 1/2 2P or 1/2 * 4
> > (even N) + 2?
>
> Huh?
I understand "=/=" means "not equal to".
In language I wrote: Twice an even number plus one is the form of
every prime other than seven and greater than two as may also be
written as one half of twice the prime or one half times four times
the even number plus two.
The equation/language hybrid expression: (Note N is even)
2 N + 1 = Primes ≠ 7 > 2 = 1/2 * 2 P = (4 N) + 2
This is my theorem. Is it valid?
>
> > Or does the single 7 present only an iceberg head in fatally flawed
> > logic?
>
> If you are asking whether there are primes other than 7 of the form 4N+3,
> then the answer is yes: e.g., 11, 19, 31, ...
>
I am not sure if I what I am inquiring equates to the above.
> In fact, there are infinitely many such primes.
>
> Best
>
> Kai-Uwe Bux
--
musatov
Kai-Uwe Bux
> On Jul 8, 7:39�pm, Kai-Uwe Bux <jkherci...@gmx.net> wrote:
>> I.N.R.I. Logic wrote:
[...]
>> > Does
>> > 2 (even N) + 1 = Every Prime =/= 7 > 2 = 1/2 2P or 1/2 * 4
>> > (even N) + 2?
>>
>> Huh?
>
> I understand "=/=" means "not equal to".
>
> In language I wrote: Twice an even number plus one is the form of
> every prime other than seven and greater than two as may also be
> written as one half of twice the prime or one half times four times
> the even number plus two.
>
> The equation/language hybrid expression: (Note N is even)
>
> 2 N + 1 = Primes ? 7 > 2 = 1/2 * 2 P = (4 N) + 2
>
> This is my theorem. Is it valid?
[...]
No. Counterexamples include 11, 19, and 31. There are infinitely many primes
that are not of the form 2*EVEN+1.
Best
Kai-Uwe Bux
mike
@d4g2000yqa.googlegroups.com>, scri...@aol.com says...
For all P > 5, P = 30*N +/- {1,7,11,13}
...with the obvious interpretation of the {} brackets.
Mike
Musatov
> In article <00e96645-4c61-491b-8a79-2a1ae4d3cf60
> @d4g2000yqa.googlegroups.com>, scribe...@aol.com says...
>
> - Show quoted text -
Neat, huh?
Bacle
This is as basic as it gets, even for people like
myself who are not number-theorists. If you cannot figure out why on your own, then you should pick up an into book on number theory before continuing to make
unfounded statements.
Read, inform yourself of the basics, and most will
have no problem answering your questions. Meeting
you halfway is not a problem as I see it; the problem
is when you expect all the effort to explain should
be made by others, so that you can be spoon-fed the
answers without doing any real effort on your part.
I don't see how this is fair.
Do your part of the work, learn the basics
and you will get better feedback.
Musatov
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"Musatov"... - comp.theory | Google Groups
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MeAmI.org
Bacle ha escrito:
> >
> > I never described myself as a prodigy. I challenge
> > any who say this
> > provide a reference.
> >
> > It is careless to make claims without citations,
> > especially when they
> > are damaging.
> >
> > Musatov
>
> http://mathforum.org/kb/thread.jspa?forumID=13&threadID=1943615&messageID=6730100#6730100
>
> And you make these unfounded claims repeatedly,
> trashing this site. This site has been going on
> for a while, with its own idiosyncrasy, and yet you
> come in and turn it into your personal playground
> of self-veneration.
Bacle the above now applies to your actions since I wrote 'Matthew
Cherian' was a prodigy not me.
As for P = NP Problem...
Basic Complexity Classes: P and NP : Good Math, Bad Math... is
arbitrarily easy; from prime factorization in RSA, to key ... As for P!
=NP, I think that is also going to be difficult, ...
Musatov. ...http://scienceblogs.com/goodmath/2007/01/
basic_complexity_classes_p_and_1.php
....Sealer....
O by 2, and take the reminder: 17=2*8+1, etc. > > > As W.Elliot said
before, for p>2 a prime: ... 1)What are all the practical reasons to
write "_term_"
Q.E.D. (?)
Vindicator2009
Dodge
M.M.M.
Dodge wrote:
> it does not work with - negative prime numbers.
Q.E.D.
Martin Musatov
M.M.M.
Vindicator2009 wrote:
> drop dead spammer
2 + 3 = 5 is prime.
QmE.D.