Re: Surrogate factoring demonstrated
From: Prai Jei (pvstownsend_at_zyx-abc.fsnet.co.uk)
Date: 03/05/05
- Previous message: myleftarmitches_at_yahoo.com: "Re: A unique number for every "person" - can it be done?"
- Maybe in reply to: Will Twentyman: "Re: Surrogate factoring demonstrated"
- Messages sorted by: [ date ] [ thread ] [ subject ] [ author ] [ attachment ]
Date: Sat, 05 Mar 2005 09:01:17 +0000
jstevh@msn.com (or somebody else of the same name) wrote thusly in message
<1109208919.921737.141190@o13g2000cwo.googlegroups.com>:
> I think it'd help to show an actual example of surrogate factoring,
> which of course is a picked example, of a case where it works.
>
> M = 105416759748241328380809513
>
> T = 260453747714406240508996639168271558799574757802353665
>
> and the factorization of T^6, needed by the current algorithm, and
> calculated by the program by calling itself recursively, until the
> numbers are small enough to be factored by a list of primes up to 300,
> is
>
>
> ( 5^6 )( 23^6 )( 61^6 )( 30557^6 )( 137573^6 )( 143881^6 )( 214213^6 )
> ( 22341796043767^6 )( 12826012523870101^6 )
>
> and the program works by iterating through combinations of those
> factors, with a special equation, and it took it 182,135 main
> iterations, as there are some other internal iterations which mean a
> maximum of 728,540 iterations, to get
>
> Number factored.
> Initial Factorization:
> f_1=247816937
> f_2=4253815781292790849
> Now checking its factors...
>
> and now the program is STILL running to try and factor f_2 as it is a
> composite, while f_1 is prime, and that's part of the problem. It's
> really slow, and doesn't reliably factor.
>
> I actually started with a smaller number which didn't factor, so I
> multiplied it by another large prime, which is part of the second
> numbers, so I call that technique using a cracking prime, but it's not
> what I consider a good approach.
>
> So you have close to a million iterations to pull out a number that's
> only a bit over 247 million itself, and that's just not very
> impressive, but it is far above chance, I think.
>
> So that's kind of a quick example of surrogate factoring kind of
> working. The program is still workong on that second factor, and I
> don't know if it will factor it or not.
>
> There's a lot of theory worked out, but much more to be figured out,
> given that it doesn't work all the time.
>
>
> James Harris
Pardon my ignorance of higher mathematics, but that sounds to me very much
as though you're starting with two numbers a and b, and attempting to show
some deep magick by which the product ab can be factorised back into a and
b without actually factorising ab itself but by working with the original a
and b.
That of course assumes a and b to be known.
Now supposing they're not known.................................
-- Paul Townsend Pair them off into threes Interchange the alphabetic letter groups to reply
- Previous message: myleftarmitches_at_yahoo.com: "Re: A unique number for every "person" - can it be done?"
- Maybe in reply to: Will Twentyman: "Re: Surrogate factoring demonstrated"
- Messages sorted by: [ date ] [ thread ] [ subject ] [ author ] [ attachment ]
Relevant Pages
|
