Re: Surrogate factoring demonstrated

From: Will Twentyman (wtwentyman_at_read.my.sig)
Date: 02/28/05 

Date: Mon, 28 Feb 2005 13:16:36 -0500

jstevh@msn.com wrote:
> Will Twentyman wrote:
>
>>jstevh@msn.com wrote:
>>
>>

>>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

This strikes me as very odd. Why would you start with those choices for
f_1 and f_2?

>
> 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.

The time data is one of the critical concerns. If it simply isn't good,
so be it. Also, are you using your method recursively to factor T? If
so, this could get very ugly as you generate T1, T2, T3, T4, ...
attempting to factor your numbers. If the time complexity is not good,
you are compounding the problem.

> 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...

It might be worthwhile to look for patterns in number of iterations to
factor a number, number of bits, number of factors, and spread between
factors.

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

That would be reflected in changes in the algorithms used.

>
> 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.

Certainly they should have, but did you ever announce *how* you were
getting the factorization of T^6? Also, if they didn't know there's a
new version, they wouldn't report that jump. Finally, there might not
be a sharp increase in factoring efficiency depending on what algorithm
is used to factor T^6. Not having looked at your code, I can't say what
happened. Did you notice such a jump in your experiments?

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

Perhaps put in a version output along with results. That should make it
easier to compare.

> 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.

There has been some personal bashing, some critiques of lack of
algorithmic analysis, and some direct computations. I don't care about
the personal bashing or boasting, as they have nothing to do with the
math. If you posted/provided your code, I'm sure that many improvements
could be offered and it would be easy to work out the time/space
complexity of your algorithm. In the limited bit of thought I've had
the chance to spend on your algorithm, I've only determined that it
isn't completely clear what the algorithm is. 

-- 
Will Twentyman
email: wtwentyman at copper dot net
Loading