Re: Surrogate factoring demonstrated

jstevh_at_msn.com
Date: 02/25/05 

Date: 24 Feb 2005 20:03:35 -0800

Will Twentyman wrote:
> jstevh@msn.com wrote:
>
> > The algorithm is so simple that it's amazing how often it does
work.
>
> What other methods have you compared it with that makes it amazing?
>
> >
> > Given a target M, you pick a j, where I now recommend picking a j
as
> > close to M as you can where j is *odd*, as I am now thinking that's
> > important, again.
> >
> > Once you've picked j, you find T, using
> >
> > T = M^2 - j^2
> >
> > and my recommendation is that T have 2, 3 and 5 as factors, and
there's
> > a theoretical reason but I'm keeping things simple here.
> >
> > Then you just iterate through integers f_1 and f_2 such that
> >
> > f_1 f_2 = T^6
> >
> > so you need to factor T, and you use that f_1 and f_2 in
> >
> > w_num = +/-(f_1 +/- f_2) - 2T^2 (2j^2 + T)
> >
> > and you take the gcd of w_num with M, and if it's not 1, then
you're
> > done.
>
>
> That's far more useful for letting us make test programs and
> benchmarking vs other methods.

Go for it.

I'm looking for data.

Here, unlike with most of my other number theory research, data best
tells the tale.

Very little to spin, just the facts of actual factoring percentages,
and comparisons with other methods.

If it's horrible, I'll just accept it, but I want real info, as I'm
tired of the propaganda.

>
> With a little effort, it should be easy to make a benchmarking
program
> to compare success rates and time to factor.
>
> >
> > That is the full algorithm. I know it looks too simple to be worth
> > anything, but if you try it, you will be amazed at the high
factoring
> > percentage--for small numbers i.e. under 40 bits.
>
> Do you have any data on how it compares with other methods either
speed
> or success wise?
>

Probably very badly. But I'd appreciate actual data nonetheless, and
while some posters *have* put up data with other algorithms, I haven't
seen much with the one that factors only T, which is the one I give in
this thread.

Here's another demonstration from my current test program which tells a
lot of why I'm suspicious of negative bashing posters:

 ( 5^6 )( 11^6 )( 67^6 )( 1753^6 )( 137573^6 )( 214213^6 )( 292393^6 )(
4197749^6 )

T=233658657807655786575865728865

Iterations: 36384

Number factored.
Initial Factorization:
f_1=15878593
f_2=54304241
Now checking its factors...
moving up a level

Success!
Factors:
 ( 15878593 )( 54304241 )
Product: 862274941012913

In coming is 862274941012913
Number of digits: 15
bitLength=50

I edit out information like time data (not good) as I'm wary of giving
the negative politicos more data to spin, as well as some specifics
that relate to details of what the program is doing and what I'm
researching currently.

Sure it's only a 50 bit number, but it did factor. I forced in factors
of 2, so the iterations max out at 8 times the number shown (though I
think the real number is a lot less...I guess I should have the
computer count).

Now I can do that with 50 bit numbers and 40 bit numbers but for some
reason things usually crap out with larger numbers, but, you see, a few
weeks ago, I couldn't do that with 50 bit numbers and 40 bit numbers as
the programs would crap out...

As I work out theory, the programs get better and faster.

So functionally I know certain people aren't exactly making sense with
their criticisms, as for instance, they should have reported a sharp
increase in factoring efficiency with the latest algorithm that only
factors T, where you need T^6, versus ALL the previous ones, with a
HUGE jump from algorithms where you factored T and j.

But they did not. It doesn't add up with the mathematical reality, so
there's something there that doesn't smell right.

And don't let bashing posters convince you otherwise until they put up
data.

Let's see more facts, and less political advertising masquerading as
cogent criticism of my theory and algorithms.

James Harris