Re: Surrogate factoring approach, analysis

mensanator at aol.compost

From:	mensanator at aol.compost
Subject:	Re: Surrogate factoring approach, analysis
Date:	21 Jan 2005 18:03:15 -0800

jstevh@msn.com wrote:

> Skipping...trivially factors as the program has a prime list up to
200.

No, it doesn't. The primes >41 are commented out.

> Same as above, as again, the program automatically will check for
> primes up to 200, so these are trivial factorizations for it, not
worth
> putting up.

Since the prime list has only 2-digit primes, what do suppose would
happen if you tested every composite that has two 3-digit factors?
None of them would be trivial. Here's what happens:

http://members.aol.com/mensanator/JSH/JSH_results.htm

> > 137305167623353
>
> ( 11173213 12288781 )
>
> Whew! It's taking a lot longer now as the program really isn't built
> for large numbers, yet. It's a proof of concept prototype not built
> for speed.

Proof of a prototype? My test results would appear to prove that
your algotithm doesn't work.

>
> I was worried it might not factor any numbers of this size.

I would be more concerned about getting it to factor small
numbers first and then see how well it does with large numbers.

>
> It is a prototype program, though it is strangely slower than I'd
hoped
> with these numbers.

Speed doesn't matter if it doesn't work.

>
> And I know, now more of you will make fun of me for such a pathetic
> result,

No mockery needed, the results speak for themselves.

> but I already said it doesn't factor everything.

That should say "doesn't even factor everything trivial".

>
> If it did, I wouldn't be talking about it publicly.
>
> The question is, what are the limits?

Three-digit factors, obviously.

> Why does it factor some numbers and not others?

That's a good question. Suppose I added the rest of the 2-digit
primes to the list. Would anything change?

> It looks from this little experiment like it's getting
> worse as the numbers get bigger which is a bad sign,

Probably because it doesn't work in theory.

> but what are the mathematical reasons why?

A better question is why does it work at all? Maybe if you
undertood that better, you would see why some numbers fall
through the cracks.

>
> Remember, this is from my theory, a theory you won't find in
textbooks,
> and if you had Newton write an algorithm based on congruence of
squares
> soon after he discovered it, would he write the Number Field Sieve?
>
> Think about it before more you yucks decide to make fun of me.
What if Newton had Java?

> James Harris