odd-perfect numbers don't exist

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• prime, prime, and double-prime... there Paul Leyland can t spam me or maybe he can!?!? Hi, Mr. Broadhurst, the fatPhil Carmody, Mr. Paul Underwood,
Message 1 of 6 , Jul 27, 2010
prime, prime, and double-prime... there Paul Leyland
can't spam me or maybe he can!?!? Hi, Mr. Broadhurst,
the fatPhil Carmody, Mr. Paul Underwood, Maximillion,
Mr. Brennen, et. al.

if you like numbers, or don't like them... just have a
look at "why odd-perfect numbers can't & don't exist."
there's a 1-page solution to a 350-year-old question.

a math friend, a math fiend, or even an enemy... just
have them check out my website. www.oddperfectnumbers.com

you'll enjoy the results... and even Dr. Carl Pomerance
like it so much that he contributed to it.

anyone can follow these ideas with just a paper, pencil
and the proper lighting; they're not hard to understand
once you adjust yourself to the wavelength!

it's a rigorous algebraic proof... a little tricky; Mr.
Peter Lesala would be proud of how I transformed his
paper into a real gem.

prime, prime, 29, 541, 7919, etc. a real gem...diamond.

Bill Bouris
• I ve pointed out one fatal flaw in the proof to you before, and you never addressed it... Where do you use the fact that the sum N = 1+f1+f2+..+f(n-1)+fn must
Message 2 of 6 , Jul 27, 2010
I've pointed out one fatal flaw in the proof to you
before, and you never addressed it... Where do you
use the fact that the sum N = 1+f1+f2+..+f(n-1)+fn must
contain *ALL* of the factors of N?

Because finding solutions where N is the sum of 1
plus some *subset* of all of its non-trivial factors,
and meeting the criterion that if x is in the subset
then so is N/x, is trivial.

Just as an example, take N = (3*7*11*13)^2*22021 =
198585576189, and take the sum of all of its factors
which are either divisible by 22021 or which are
coprime to 22021. Or to put it another way, this
number N would be an odd perfect number if only the
number 22021 were prime.

Until your proof uses the fact that the sum N must
contain all of the factors of N, it's not worth
analyzing to be honest...

leavemsg1 wrote:
> prime, prime, and double-prime... there Paul Leyland
> can't spam me or maybe he can!?!? Hi, Mr. Broadhurst,
> the fatPhil Carmody, Mr. Paul Underwood, Maximillion,
> Mr. Brennen, et. al.
>
> if you like numbers, or don't like them... just have a
> look at "why odd-perfect numbers can't & don't exist."
> there's a 1-page solution to a 350-year-old question.
>
> a math friend, a math fiend, or even an enemy... just
> have them check out my website. www.oddperfectnumbers.com
>
> you'll enjoy the results... and even Dr. Carl Pomerance
> made a contribution to this happy find. He read it and
> like it so much that he contributed to it.
>
> anyone can follow these ideas with just a paper, pencil
> and the proper lighting; they're not hard to understand
> once you adjust yourself to the wavelength!
>
> it's a rigorous algebraic proof... a little tricky; Mr.
> Peter Lesala would be proud of how I transformed his
> paper into a real gem.
>
> prime, prime, 29, 541, 7919, etc. a real gem...diamond.
>
> Bill Bouris
>
>
>
> ------------------------------------
>
> Unsubscribe by an email to: primenumbers-unsubscribe@yahoogroups.com
> The Prime Pages : http://www.primepages.org/
>
>
>
>
>
>
• Note that the smallest non-square N which permits a subset of that form that sums to N is N=12285: What does your proof say about the existence of this sum:
Message 3 of 6 , Jul 27, 2010
Note that the smallest non-square N which permits a subset of
that form that sums to N is N=12285:

sum:

12285 = 1+
3+5+7+9+15+21+39+45+65+105+
117+189+273+315+585+819+1365+1755+2457+4095

Jack Brennen wrote:
> I've pointed out one fatal flaw in the proof to you
> before, and you never addressed it... Where do you
> use the fact that the sum N = 1+f1+f2+..+f(n-1)+fn must
> contain *ALL* of the factors of N?
>
> Because finding solutions where N is the sum of 1
> plus some *subset* of all of its non-trivial factors,
> and meeting the criterion that if x is in the subset
> then so is N/x, is trivial.
>
> Just as an example, take N = (3*7*11*13)^2*22021 =
> 198585576189, and take the sum of all of its factors
> which are either divisible by 22021 or which are
> coprime to 22021. Or to put it another way, this
> number N would be an odd perfect number if only the
> number 22021 were prime.
>
> Until your proof uses the fact that the sum N must
> contain all of the factors of N, it's not worth
> analyzing to be honest...
>
>
>
> leavemsg1 wrote:
>> prime, prime, and double-prime... there Paul Leyland
>> can't spam me or maybe he can!?!? Hi, Mr. Broadhurst,
>> the fatPhil Carmody, Mr. Paul Underwood, Maximillion,
>> Mr. Brennen, et. al.
>>
>> if you like numbers, or don't like them... just have a
>> look at "why odd-perfect numbers can't & don't exist."
>> there's a 1-page solution to a 350-year-old question.
>>
>> a math friend, a math fiend, or even an enemy... just
>> have them check out my website. www.oddperfectnumbers.com
>>
>> you'll enjoy the results... and even Dr. Carl Pomerance
>> made a contribution to this happy find. He read it and
>> like it so much that he contributed to it.
>>
>> anyone can follow these ideas with just a paper, pencil
>> and the proper lighting; they're not hard to understand
>> once you adjust yourself to the wavelength!
>>
>> it's a rigorous algebraic proof... a little tricky; Mr.
>> Peter Lesala would be proud of how I transformed his
>> paper into a real gem.
>>
>> prime, prime, 29, 541, 7919, etc. a real gem...diamond.
>>
>> Bill Bouris
>>
>>
>>
>> ------------------------------------
>>
>> Unsubscribe by an email to: primenumbers-unsubscribe@yahoogroups.com
>> The Prime Pages : http://www.primepages.org/
>>
>>
>>
>>
>>
>>
>
>
>
> ------------------------------------
>
> Unsubscribe by an email to: primenumbers-unsubscribe@yahoogroups.com
> The Prime Pages : http://www.primepages.org/
>
>
>
>
>
>
• Jack, please visit my website... www.oddpefectnumbers.com to see if we agree on how I ve presented my proof. we can talk privately. let s take it in bit
Message 4 of 6 , Jul 12, 2011
Jack,

www.oddpefectnumbers.com to see if we
agree on how I've presented my proof.
we can talk privately. let's take it
in bit pieces, and I'll walk you thru
the logic.

my e-mail is leavemsg1@...

Bill
• Hi, Dr. Smith, I got it!!!!!!!!!!!!!!!... here it is... you can visit my website... www.oddperfectnumbers.com. or read below. ... for those of you that have
Message 5 of 6 , Dec 5, 2011
Hi, Dr. Smith,

I got it!!!!!!!!!!!!!!!... here it is...
you can visit my website... www.oddperfectnumbers.com.
...
for those of you that have visited my website, I've spent
the last 10 years (almost 100 drafts) searching for a rea-
sonable explanation for why odd-perfect numbers don't exist,
and here it is...
...
a puzzle of antiquity, fittingly solved, if you will...
using simple algebra.
...
the first few 'perfect' numbers are 6, 28, 496, and 8128.
Euler proved that they were all of the form... N= (2^(n-1))
*(2^n -1), he knew that the (2^n -1) portion had to always
be prime, and he also noted that sigma(N) = 2N when N is a
'perfect' number. Notice how I'm putting the quotations
around the word 'perfect'.
...
the situation was more perfect than you might imagine, and
I'm sure that you will be convinced that Euler's famous form-
ula cannot be altered as he mentioned in order to produce an
odd-perfect number! Here's what was missing...
... 2*t t - 2
_________ _________
\ \
\ \
N=(2^t)*(2^(t +1) -1) = } 2^r - } 2^s ; (t +1)= p
from a Mersenne prime / /
/________ /________
r= 1 s= 1
...
(OR) 6 = 2^1 +2^2 -(0),
28 = 2^1 +2^2 +2^3 +2^4 -(2^1),
496 = 2^1 +2^2 +2^3 +2^4 +2^5 +2^6 +2^7 +2^8 - (2^3 +2^2 +2^1),
8128 = etc.
...
when 'N' is 'perfect', 'N' is equal to the sum (or rather the
difference) of two summations that are purely binary. It was
more delicate that previously thought. Changing the base from
'2' to something else would be the only meaningful change to
such a demanding, connective equation, and that leads us to the
conclusion that an 'odd-perfect-number notion' is out of the
question, and can't be 'perfect'.
...
thus, odd-perfect numbers don't exist!
...
obviously, when someone as prolific as Euler stated that this
problem was too complicated to be easily solved, every mathema-
tician was easily pursuaded to believe it; but if you (OR) I
decided to retain Euler's already-proven formula for an odd-
perfect number, it's surprising to me that we could have been
...
*QED
Bill Bouris
12/5/2011
...
• Message 6 of 6 , Dec 5, 2011
> ... this's more readable, I hope.
>............................2*t...........t - 2
>........................._________......_________
>.........................\..............\
>..........................\..............\
> N=(2^t)*(2^(t +1) -1) =...}..2^r...-.....}..2^s....; (t +1)= p
> from a Mersenne prime..../............../
>........................./________....../________
>............................r= 1...........s= 1
> ...

--- In primenumbers@yahoogroups.com, "leavemsg1" <leavemsg1@...> wrote:
>
> Hi, Dr. Smith,
>
> I got it!!!!!!!!!!!!!!!... here it is...
> you can visit my website... www.oddperfectnumbers.com.
> ...
> for those of you that have visited my website, I've spent
> the last 10 years (almost 100 drafts) searching for a rea-
> sonable explanation for why odd-perfect numbers don't exist,
> and here it is...
> ...
> a puzzle of antiquity, fittingly solved, if you will...
> using simple algebra.
> ...
> the first few 'perfect' numbers are 6, 28, 496, and 8128.
> Euler proved that they were all of the form... N= (2^(n-1))
> *(2^n -1), he knew that the (2^n -1) portion had to always
> be prime, and he also noted that sigma(N) = 2N when N is a
> 'perfect' number. Notice how I'm putting the quotations
> around the word 'perfect'.
> ...
> the situation was more perfect than you might imagine, and
> I'm sure that you will be convinced that Euler's famous form-
> ula cannot be altered as he mentioned in order to produce an
> odd-perfect number! Here's what was missing...
>............................2*t...........t - 2
>........................._________......_________
>.........................\..............\
>..........................\..............\
> N=(2^t)*(2^(t +1) -1) =...}..2^r...-.....}..2^s....; (t +1)= p
> from a Mersenne prime..../............../
>........................./________....../________
>............................r= 1...........s= 1
> ...
> (OR) 6 = 2^1 +2^2 -(0),
> 28 = 2^1 +2^2 +2^3 +2^4 -(2^1),
> 496 = 2^1 +2^2 +2^3 +2^4 +2^5 +2^6 +2^7 +2^8 - (2^3 +2^2 +2^1),
> 8128 = etc.
> ...
> when 'N' is 'perfect', 'N' is equal to the sum (or rather the
> difference) of two summations that are purely binary. It was
> more delicate that previously thought. Changing the base from
> '2' to something else would be the only meaningful change to
> such a demanding, connective equation, and that leads us to the
> conclusion that an 'odd-perfect-number notion' is out of the
> question, and can't be 'perfect'.
> ...
> thus, odd-perfect numbers don't exist!
> ...
> obviously, when someone as prolific as Euler stated that this
> problem was too complicated to be easily solved, every mathema-
> tician was easily pursuaded to believe it; but if you (OR) I
> decided to retain Euler's already-proven formula for an odd-
> perfect number, it's surprising to me that we could have been
> mislead by his prior conclusion!
> ...
> *QED
> Bill Bouris
> 12/5/2011
> ...
>
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