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Topic: borderline of finite with infinite Chapt13.40085 Maxwell Equations
placing demands on mathematics #631 New Physics #751 ATOM TOTALITY 5th ed

Replies: 54   Last Post: Jun 29, 2012 1:48 PM

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Transfer Principle

Posts: 330
Registered: 9/4/11
Re: 120^288 and how to get it nearer to 10^604 Chapt13.40085 Maxwell
Equations placing demands on mathematics #651 New Physics #771 ATOM TOTALITY
5th ed

Posted: Jun 19, 2012 5:45 PM
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On Jun 19, 3:19 am, Archimedes Plutonium
<plutonium.archime...@gmail.com> wrote:
> On Jun 19, 3:47 am, "io_x" <a...@b.c.invalid> wrote:
> > here this is ok
> > (16) -> c:=(120 ^ 291)/  81
> >    (16)
> >   135911930413328771927856248088227273330584837917347940523287916343518691899 9_
> >    690585504819382216526236402082584790197171041378399859102382461453415865321 _
> >    289342578352265056153572709886088953858778381318346248947192203901956277713 _
> >    062733148570612814040537186033993596502486544301179402174908486464784319131 _
> >    505496424448000000000000000000000000000000000000000000000000000000000000000 _
> >    000000000000000000000000000000000000000000000000000000000000000000000000000 _
> >    000000000000000000000000000000000000000000000000000000000000000000000000000 _
> >    000000000000000000000000000000000000000000000000000000000000000000000000000 _
> >    000

> Io, division will not work because it leads to fractions

Normally, division will indeed lead to fractions, but not in
this case, because we can take advantage of powers.

Notice that 120 factors as 2^3*3*5. This means that we have:

120^291 = 2^(3*291) * 3^291 * 5^291
= 2^873 * 3^291 * 5^291

So there are lots of factors of three around, making division
very simple indeed. Of course, AP subsequently corrected his
mistake, and so we want to divide by 27, not 81 here:

120^291/27 = 2^873 * 3^288 * 5^291

This number is a perfect cube and is exactly three times the
number that Io produced above.

> There maybe a 9.999.. x 10^603 type of perfect cube factorable by 120.

Indeed there is. Notice that if a number is divisible by 2*3*5
(which equals thirty), its cube will have 2^3 * 3^3 * 5^3 as a
factor, and therefore 2^3 * 3 * 5 (which is 120) as well. This
gives us a recipe for finding a cube of the form 9.999...*10^603
that has 120 as a factor:

-- Begin with the number 10^604.
-- Take its cube root and discard everything after the decimal.
-- Divide by thirty and discard everything after the decimal.
-- Multiply it by thirty.
-- Cube it.

The resulting number will be the largest cube less than 10^603
with 120 as a factor. As it turns out, this number is approx.
10^604 - 2.111213954...*10^404, so there are 199 nines before
the first digit other than nine. (This is expected since the
d/dx(x^3) is 3x^2, so we expect the largest cube less than
10^604 to be on the order of 10^402 away. The extra two orders
taking us to 10^404 is due to the additional constraint that
the cube have 120 as a factor.)

Of course, most of AP's cubes weren't divisible merely by 120,
but by large powers of 120. It turns out that the number that
we just found happens to have 120^2 as a factor, but no more
factors of 120. (Due to excess powers of two, finding cubes
divisible by 120^2 or 120^3 are not uncommon by this method,
but we must be especially lucky to find 120^4.)

Most likely, the cube that we just found won't help AP much,
but it does provide an answer to his question.

Meanwhile, I noticed that Io started a thread looking for
factors of floor(pi*10^603) beyond the ones that he found (I
presume by trial division). Such factors will be difficult,
since the number to be factored is only a few orders shy of
the RSA numbers. (This is why the link that I provided earlier
stops at 250, with about half of those incompletely factored.)


Date Subject Author
6/15/12
Read borderline of finite with infinite Chapt13.40085 Maxwell Equations
placing demands on mathematics #631 New Physics #751 ATOM TOTALITY 5th ed
plutonium.archimedes@gmail.com
6/15/12
Read Ludwig Poehl's aka Archie-pooh's own personal Idiot Quotient
hanson
6/15/12
Read borderline of finite with infinite Chapt13.40085 Maxwell Equations
placing demands on mathematics #632 New Physics #752 ATOM TOTALITY 5th ed
plutonium.archimedes@gmail.com
6/15/12
Read pi borderline of finite with infinite Chapt13.40085 Maxwell Equations
placing demands on mathematics #633 New Physics #753 ATOM TOTALITY 5th ed
plutonium.archimedes@gmail.com
6/16/12
Read where pi is a whole number square root and cube root and a proof
Chapt13.40085 Maxwell Equations placing demands on mathematics #634 New
Physics #754 ATOM TOTALITY 5th ed
plutonium.archimedes@gmail.com
6/18/12
Read Re: pi borderline of finite with infinite Chapt13.40085 Maxwell Equations placing demands on mathematics #633 New Physics #753 ATOM TOTALITY 5th ed
adrian dogsbody
6/18/12
Read Re: pi borderline of finite with infinite Chapt13.40085 Maxwell
Equations placing demands on mathematics #642 New Physics #762 ATOM TOTALITY
5th ed
plutonium.archimedes@gmail.com
6/19/12
Read Re: pi borderline of finite with infinite Chapt13.40085 Maxwell Equations placing demands on mathematics #642 New Physics #762 ATOM TOTALITY 5th ed
adrian dogsbody
6/19/12
Read Re: pi borderline of finite with infinite Chapt13.40085 Maxwell
Equations placing demands on mathematics #642 New Physics #762 ATOM TOTALITY
5th ed
plutonium.archimedes@gmail.com
6/18/12
Read Re: pi borderline of finite with infinite Chapt13.40085 Maxwell
Equations placing demands on mathematics #633 New Physics #753 ATOM TOTALITY
5th ed
plutonium.archimedes@gmail.com
6/19/12
Read Re: pi borderline of finite with infinite Chapt13.40085 Maxwell Equations placing demands on mathematics #633 New Physics #753 ATOM TOTALITY 5th ed
adrian dogsbody
6/19/12
Read 120^291 and how to get it nearer to 10^603 Chapt13.40085 Maxwell
Equations placing demands on mathematics #648 New Physics #768 ATOM TOTALITY
5th ed
plutonium.archimedes@gmail.com
6/19/12
Read 120^288 and how to get it nearer to 10^603 Chapt13.40085 Maxwell
Equations placing demands on mathematics #649 New Physics #769 ATOM TOTALITY
5th ed
plutonium.archimedes@gmail.com
6/19/12
Read 120^288 and how to get it nearer to 9*10^603 Chapt13.40085 Maxwell
Equations placing demands on mathematics #650 New Physics #770 ATOM TOTALITY
5th ed
plutonium.archimedes@gmail.com
6/19/12
Read Re: 120^291 and how to get it nearer to 10^603 Chapt13.40085 Maxwell Equations placing demands on mathematics #648 New Physics #768 ATOM TOTALITY 5th ed
adrian dogsbody
6/19/12
Read 120^288 and how to get it nearer to 10^604 Chapt13.40085 Maxwell
Equations placing demands on mathematics #651 New Physics #771 ATOM TOTALITY
5th ed
plutonium.archimedes@gmail.com
6/19/12
Read infinity borderline at 9.4x10^603 and proof by pseudosphere
Chapt13.40085 Maxwell Equations placing demands on mathematics #652 New
Physics #772 ATOM TOTALITY 5th ed
plutonium.archimedes@gmail.com
6/19/12
Read Re: 120^288 and how to get it nearer to 10^604 Chapt13.40085 Maxwell
Equations placing demands on mathematics #651 New Physics #771 ATOM TOTALITY
5th ed
Transfer Principle
6/19/12
Read Re: 120^288 and how to get it nearer to 10^604 Chapt13.40085 Maxwell
Equations placing demands on mathematics #653 New Physics #773 ATOM TOTALITY
5th ed
plutonium.archimedes@gmail.com
6/20/12
Read infinity starts at 9.999..x10^603 just shy of 10^604; tractrix proof
Chapt13.40085 Maxwell Equations placing demands on mathematics #654 New
Physics #774 ATOM TOTALITY 5th ed
plutonium.archimedes@gmail.com
6/20/12
Read Riemann zeta equalling Euler Zeta is another proof Chapt13.40085
Maxwell Equations placing demands on mathematics #655 New Physics #775 ATOM
TOTALITY 5th ed
plutonium.archimedes@gmail.com
6/20/12
Read Pseudosphere/tractrix proof demand that infinity is floor pi *10^603
Chapt13.40085 Maxwell Equations placing demands on mathematics #656 New
Physics #776 ATOM TOTALITY 5th ed
plutonium.archimedes@gmail.com
6/20/12
Read Re: Pseudosphere/tractrix proof demand that infinity is floor pi
*10^603 Chapt13.40085 Maxwell Equations placing demands on mathematics #656
New Physics #776 ATOM TOTALITY 5th ed
plutonium.archimedes@gmail.com
6/21/12
Read calculus maybe able to prove pseudosphere area with infinity at
9.99..x10^603 Chapt13.40085 Maxwell Equations placing demands on mathematics
#657 New Physics #777 ATOM TOTALITY 5th ed
plutonium.archimedes@gmail.com
6/21/12
Read Re: calculus maybe able to prove pseudosphere area with infinity
at 9.99..x10^603 Chapt13.40085 Maxwell Equations placing demands on mathematics
#657 New Physics #777 ATOM TOTALITY 5th ed
Jos Bergervoet
6/21/12
Read second method proof pseudosphere area with infinity at 9.99..x10^603
Chapt13.40085 Maxwell Equations placing demands on mathematics #658 New
Physics #778 ATOM TOTALITY 5th ed
plutonium.archimedes@gmail.com
6/21/12
Read Re: second method proof pseudosphere area with infinity at
9.99..x10^603 Chapt13.40085 Maxwell Equations placing demands on mathematics
#659 New Physics #779 ATOM TOTALITY 5th ed
plutonium.archimedes@gmail.com
6/22/12
Read Re: second method proof pseudosphere area with infinity at 9.99..x10^603 Chapt13.40085 Maxwell Equations placing demands on mathematics #659 New Physics #779 ATOM TOTALITY 5th ed
adrian dogsbody
6/22/12
Read tractrix/pseudosphere proof with infinity at 9.99..x10^603
Chapt13.40085 Maxwell Equations placing demands on mathematics #660 New
Physics #780 ATOM TOTALITY 5th ed
plutonium.archimedes@gmail.com
6/22/12
Read Re: tractrix/pseudosphere proof with infinity at 9.99..x10^603
Chapt13.40085 Maxwell Equations placing demands on mathematics #661 New
Physics #781 ATOM TOTALITY 5th ed
plutonium.archimedes@gmail.com
6/25/12
Read Re: tractrix/pseudosphere proof with infinity at 9.99..x10^603 Chapt13.40085 Maxwell Equations placing demands on mathematics #660 New Physics #780 ATOM TOTALITY 5th ed
adrian dogsbody
6/25/12
Read Re: tractrix/pseudosphere proof with infinity at 9.99..x10^603
Chapt13.40085 Maxwell Equations placing demands on mathematics #660 New
Physics #780 ATOM TOTALITY 5th ed
narasimham
6/20/12
Read Re: 120^288 and how to get it nearer to 10^604 Chapt13.40085 Maxwell Equations placing demands on mathematics #651 New Physics #771 ATOM TOTALITY 5th ed
adrian dogsbody
6/28/12
Read Re: 120^288 and how to get it nearer to 10^604 Chapt13.40085 Maxwell
Equations placing demands on mathematics #651 New Physics #771 ATOM TOTALITY
5th ed
Transfer Principle
6/29/12
Read floor(tau*10^603)
quasi
6/29/12
Read Re: 120^288 and how to get it nearer to 10^604 Chapt13.40085 Maxwell Equations placing demands on mathematics #651 New Physics #771 ATOM TOTALITY 5th ed
adrian dogsbody
6/16/12
Read Re: borderline of finite with infinite Chapt13.40085 Maxwell
Equations placing demands on mathematics #631 New Physics #751 ATOM TOTALITY
5th ed
Transfer Principle
6/17/12
Read Re: borderline of finite with infinite Chapt13.40085 Maxwell
Equations placing demands on mathematics #637 New Physics #757 ATOM TOTALITY
5th ed
plutonium.archimedes@gmail.com
6/17/12
Read Re: borderline of finite with infinite Chapt13.40085 Maxwell
Equations placing demands on mathematics #638 New Physics #758 ATOM TOTALITY
5th ed
plutonium.archimedes@gmail.com
6/17/12
Read Re: borderline of finite with infinite Chapt13.40085 Maxwell
Equations placing demands on mathematics #638 New Physics #758 ATOM TOTALITY
5th ed
Transfer Principle
6/17/12
Read Re: borderline of finite with infinite Chapt13.40085 Maxwell
Equations placing demands on mathematics #639 New Physics #759 ATOM TOTALITY
5th ed
plutonium.archimedes@gmail.com
6/18/12
Read method of predicting the digits of pi?? Chapt13.40085 Maxwell
Equations placing demands on mathematics #640 New Physics #760 ATOM TOTALITY
5th ed
plutonium.archimedes@gmail.com
6/18/12
Read Re: method of predicting the digits of pi?? Chapt13.40085 Maxwell
Equations placing demands on mathematics #640 New Physics #760 ATOM TOTALITY
5th ed
KBH
6/18/12
Read Re: method of predicting the digits of pi?? Chapt13.40085 Maxwell
Equations placing demands on mathematics #640 New Physics #760 ATOM TOTALITY
5th ed
KBH
6/18/12
Read Re: method of predicting the digits of pi?? Chapt13.40085 Maxwell
Equations placing demands on mathematics #640 New Physics #760 ATOM TOTALITY
5th ed
KBH
6/18/12
Read reverse engineering Chapt13.40085 Maxwell Equations placing demands
on mathematics #641 New Physics #761 ATOM TOTALITY 5th ed
plutonium.archimedes@gmail.com
6/18/12
Read engineering the borderline of finite to infinite Chapt13.40085
Maxwell Equations placing demands on mathematics #643 New Physics #763 ATOM
TOTALITY 5th ed
plutonium.archimedes@gmail.com
6/18/12
Read Re: engineering the borderline of finite to infinite Chapt13.40085
Maxwell Equations placing demands on mathematics #644 New Physics #764 ATOM
TOTALITY 5th ed
plutonium.archimedes@gmail.com
6/18/12
Read Re: engineering the borderline of finite to infinite Chapt13.40085
Maxwell Equations placing demands on mathematics #645 New Physics #765 ATOM
TOTALITY 5th ed
plutonium.archimedes@gmail.com
6/18/12
Read Re: engineering the borderline of finite to infinite Chapt13.40085
Maxwell Equations placing demands on mathematics #643 New Physics #763 ATOM
TOTALITY 5th ed
Transfer Principle
6/18/12
Read 120^291 (1.1*10^605) as infinity borderline Chapt13.40085 Maxwell
Equations placing demands on mathematics #646 New Physics #766 ATOM TOTALITY
5th ed
plutonium.archimedes@gmail.com
6/18/12
Read Re: 120^291 (1.1*10^605) as infinity borderline Chapt13.40085 Maxwell
Equations placing demands on mathematics #647 New Physics #767 ATOM TOTALITY
5th ed
plutonium.archimedes@gmail.com
6/18/12
Read Re: method of predicting the digits of pi?? Chapt13.40085 Maxwell Equations placing demands on mathematics #640 New Physics #760 ATOM TOTALITY 5th ed
Bob Masta
6/17/12
Read Re: borderline of finite with infinite Chapt13.40085 Maxwell
Equations placing demands on mathematics #637 New Physics #757 ATOM TOTALITY
5th ed
Transfer Principle
6/19/12
Read Re: borderline of finite with infinite Chapt13.40085 Maxwell Equations placing demands on mathematics #637 New Physics #757 ATOM TOTALITY 5th ed
adrian dogsbody

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