## Re: odd-perfect numbers don't exist

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• Message 1 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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