Re: Surrogate factoring, theory versus implementation
jstevh_at_msn.com
Date: 01/26/05
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Date: 25 Jan 2005 15:12:12 -0800
Michael Brown wrote:
> jstevh@msn.com wrote:
> [...]
>
> Repeating from an earlier post that probably got lost in the morass
of other
> posts:
I remember replying to it.
Oh, and some posters seem to make replies deliberately to try and
obscure the actual mathematical topic, while mainly just ridiculing me
and my work, which is how posts can get lost.
Notice how they've piled on already in this thread.
I suggest to you it's a deliberate strategy, meant to confuse and
obscure.
They're obsessive little demons.
>
> [[BEGIN REPEAT]]
>
> For what it's worth, I cooked up a couple of ~64-bit primes (was a
104-bit
> product, I forgot to set the uppermost bits). They weren't specially
chosen
> or even well-generated. I just used the rand() function to generate a
binary
> string. Their product was 17417537469613251264524569748998981537.
"factor"
> from:
> http://www.asahi-net.or.jp/~KC2H-MSM/cn/
> factored it in 33.26 seconds (1128714656609730623 *
15431302648208293919).
> After a bit of trial and error, it turned out that it could factor
the
> product squared minus 16 in 3.26 seconds:
>
303370611505381579716912725262028356146608169452120680027239449463266882353
> = 3* 3 * 71 * 307 * 2673397 * 84828952219129 * 8533686513259849 *
> 799079573776815674841701598797953
>
> How do you get the original primes from the above factorisation? Or
does j
> have to be specially chosen?
So far I have that M and j need to match in terms of being even or odd,
so if M is even then j needs to be even, and if M is odd then j needs
to be odd.
Other than that, you can basically pick j at will.
>
> [[END REPEAT]]
>
> And I followed up with:
>
> [[BEGIN REPEAT]]
>
> Michael Brown wrote:
> [...]
> > How do you get the original primes from the above factorisation? Or
> > does j have to be specially chosen?
>
> From what I can gather, it's supposed to go something like:
> b_i = factors of j^2 ( = 16 in this case)
> f_i = factors of T (product squared minus j^2)
>
> b_1 = product of some subset of b_i
> b_2 = -j^2 / b1
I noted in my other reply that these are *rationals* so you have an
infinite set here.
> f_1 = product of some subset of f_i
> f_2 = T / f_1
>
These are integers. So you have a finite set.
> A = some integer (not sure how to calculate this)
>
The paper shows that A is mostly irrelevant, though my latest research
indicates it can impact in a special way.
I now think that just letting A=1 is the simplest way to go, so you can
forget about it.
> Then a possible factor is:
> (b_1 f_2 + b_2 f_1 + 2 j^2) / A
>
> Since I'm not sure how to calculate A, I just calculated each
possibility
> mod each of the original primes to see if it was zero. No such
combination
> occured (except for the trivial cases b_1 = f_1 = 1 or the prime to
be
> tested was zero).
You didn't test infinity.
There are an *infinite* number of possible b's, as they are in
rationals.
Now my theory shows how the mathematics traverses that infinite set and
picks out a finite subset of it, which is how it's a super sieve, like
nothing ever seen before besides the Shor algorithm, with quantum
computing.
That mathematics is really neat.
>
> Is my interpretation correct?
>
You're stuck on the b's not being integers, as from your post it sounds
like you used integers for them.
They are not typically integers, but are usually fractions.
> [[END REPEAT]]
>
> --
> Michael Brown
> www.emboss.co.nz : OOS/RSI software and more :)
> Add michael@ to emboss.co.nz ---+--- My inbox is always open
There's no way you'll get a handle on the mathematics without going
over it in detail and Usenet is not the way to go.
I have put all the information that you need at
http://groups.yahoo.com/group/sufactor/
where you'll notice a significantly better signal to noise ratio, as
I'm just about the only person posting, and as there's no need to deal
with nasty obsessive demon posters, I can just talk math.
If you have an ounce of mathematical curiosity then you should wish to
know how in the hell b_1 and b_2 can be fractions!!!
It's beautiful mathematics.
James Harris
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