Re: Basically a sieve method, relation to quantum

jstevh_at_msn.com
Date: 01/24/05 

Date: 24 Jan 2005 15:09:51 -0800

Michael Brown wrote:
> 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

It's a rational, typically a fraction.

> b_2 = -j^2 / b1

It's a rational, typically a fraction.

> f_1 = product of some subset of f_i
> f_2 = T / f_1
>

They are both integers.

> A = some integer (not sure how to calculate this)

It's value doesn't usually matter though it can intefere.

Safest is to just set it to 1.

> 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

There's now way you calculated each possible as the b's are fractions.

Are you saying you iterated through an infinite set?

> occured (except for the trivial cases b_1 = f_1 = 1 or the prime to
be
> tested was zero).
>
> Is my interpretation correct?
>

See above.

Read the paper.

See http://groups.yahoo.com/group/sufactor/

I use the field of rationals.

The results I use are in the field of rationals.

Now then, yes, despite my use of the field of rationals, I get integers
out, as I get prime factors of the target number.

You people need to understand that the methods I'm using are new, and
some of your long-held notions of what's possible are just wrong.

Sure, you probably don't think someone can work out of the field of
rationals to figure out factorizations.

But I do. The algorithm I use in checking for prime factors of the
target goes through *every* possible RATIONAL value of the b's.

Yes, it goes through the entire infinite set, which is why I call it a
super sieve.

That's an easy enough claim to verify. If you didn't know even that
much, you don't know anything of import about surrogate factoring.
James Harris

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