Re: Ultimate check, new way to factor or not?

jstevh_at_msn.com
Date: 01/27/05 

Date: 26 Jan 2005 18:46:16 -0800

Gregory G Rose wrote:
> In article <1106787329.830488.269890@c13g2000cwb.googlegroups.com>,
> <jstevh@msn.com> wrote:
> >Did I find a new way to factor or not?
>
> You seem to have found a way to factor. I don't
> know whether it is a new way or not.
>
> But, you know, a new *inefficient* way to factor
> simply isn't interesting.

How fast was congruence of squares when discovered?

Do you even know who discovered it?

>What you haven't done is
> demonstrate your repeated claim that it is
> polynomial time. Since it can only increase the

That's easily done and has to do with the number of combinations
generated at each level of calculation, where I mean recursion level.

It's just not worth going into more detail than that now.

> size of the surrogate target, you have to end up
> factoring something with a different method, and
> the only known different methods are more than
> polynomial time. Therefore I conclude that your

That's not exactly true.

Besides, I don't have to use different methods to factor T, as in fact,
my prototype program recursively calls itself--shrinking numbers all
the way--until it gets to something under 200, at which point is uses a
prime list.

So I know you're not paying attention, already, or you'd have known
that without me having to repeat it here.

Now, factoring is in general hard, with *certain* types of numbers,
while not necessarily so with others.

My surrogate T, is offset from M, the target by the formula

T = M^2 - j^2

which factors somewhat, immediately into

T = (M-j)(M+j)

where for positive j, M-j is necessarily less than M, and M+j can be
*given* whatever factor you wish by picking j appropriately, so that
you can factor it immediately to shrink the number.

There are any number of smart things you can do when you can have as
much control as my method gives.

Now I don't see posters talking about that, as you're not interested in
the mathematics or what's possible, but only in trying to dismiss my
discovery.

But you're wasting your time, as mainstream mathematicians will try to
ignore it anyway, no matter what you do, so your effort is pointless.

> method cannot be polynomial time. Now, if it's
> subexponential, it could still be interesting, but
> you haven't argued for that, either.
>

There are only so many factoring methods known, even inefficient ones,
while certain key features of my discovery make it very exciting, and
make it definite that an inefficiency claim at this point is
short-sighted.

That you jump to a conclusion isn't a surprise to me.

You just have something you wish to believe and can't pause for even a
moment to let facts gather before you jump in with your opinion, even
when it defies the mathematics.

I, on the other hand, have worked out a lot of the theory, and the
theory says that this factoring method is in fact a solution to the
factoring problem.

That is a statement of mathematical fact. If you don't believe it's
mathematical fact then you have the route of proving your disbelief
mathematically.

There are a LOT of little proofs that I've ran through at this point in
order to come to my conclusion, many of them extraordinary in terms of
what the mathematics shows MUST be true.

For that reason, I can confidently state--before there's an
implementation that I know of which shows this--that the factoring
problem has been solved and it's now just a matter of time before the
implementation demonstrating that is out there.

You can debate about it all you want, but like I said earlier today,
I'm just goofing off, as the hard theoretical work--I think--is done.

In the end, the real world will determine the truth as factoring is
important in the real world, and your opinions, thoughts or feelings
have no impact here.

In the meantime, sure, chattering about it can be fun, but it's not
substantive.

James Harris

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