Re: JSH: Mystery increases

On Sun, 1 Mar 2009 09:50:08 -0800 (PST), JSH <jstevh@xxxxxxxxx> wrote:

On Mar 1, 2:28 am, rossum <rossu...@xxxxxxxxxxxx> wrote:
On Sat, 28 Feb 2009 15:55:17 -0800 (PST), JSH <jst...@xxxxxxxxx>
wrote:



On Feb 28, 3:29 pm, rossum <rossu...@xxxxxxxxxxxx> wrote:
On Sat, 28 Feb 2009 13:26:32 -0800 (PST), JSH <jst...@xxxxxxxxx>
wrote:

I was actually very surprised at the arguments that ensued over my
solution to the factoring problem.

It is a very simple argument with a rather basic proof, so why were
posters so diligent in throwing up distractions around it, or in
making false statements?

Your proof is incomplete.  Any solution to the factoring problem has
to be *fast*; a slow method is not a solution to the problem.

The mathematics shows that you can factor a composite D, about as fast
as you can factor D-1.

No James, you need to be more accurate in your statements here.  You
say you can find a single non-trivial factor of D after you have found
many or all of the factor pairs of D-1.  You have said that you need
to search through all possible f1, f2 pairs where f1 * f2 = d-1.  In

Not necessarily. It's just not given which will work, so potentially
you might need them all.
Thank you for agreeing with my point: "you might need them all".


general you need to know all the factors of D-1 which is slower than
just finding a single factor pair of D.

I said, about as fast as factoring D-1, and if D is an odd, then you
get a factor of D-1 immediately: 2

So you can recurse! To factor D-1 you can divide off 2, and then
factor (D-1)/2, to factor it, you may need (D-1)/2 - 1 factored, but
you can divide by 2. Get it yet?
Yes, I am aware of the potential recursion. However without the
correct equations I cannot complete even the first step of the
recursion so at the moment recursion is in practice useless.


The proof shows that one of the combinations of factors of D-1 must
give a non-trivial factorization of D at a minimum point easily
calculated and now given in the thread where Michael is stepping
through the algorithm.

You have said nothing about how fast it will be to completely factor
D-1 and it seems clear from the discussion here that finding the
minimum point you need is not a trivial task.  You still have work to
do here James.

I've given mathematical proof.

What's interesting to me is that with the proof I can easily refute
false claims.

For instance, posters continually present equations for r(v) - t(v)
which cannot give a key value that is easily shown to exist.
So just ask yourself why posters have to present their own equations
for r(v) and t(v)? It is because you have not told us what the
correct equations are James. This is your method so you need to tell
us what the correct equations are. Without the correct equations your
proof is incomplete. You have shown that they exist but not what they
are.

I can show that the factors of an RSA number exist, but that does not
tell me what those factors are.

You need to tell us what the equations are James otherwise your proof
is merely an existence proof, and that is of no use in solving the
factoring problem. We already know that a composite number has
non-trivial factors. We need to find those factors and to do that we
need the right equations. Tell us what the right equations are James.


Which destroys your claim about the poster Tim Smith's attempt in this
thread.

The equations he gives cannot handle the case where r+t = 5, and r-t =
3., which gives r = 4, t = 1.

OR do you disagree?
I agree that Tim's equations cannot handle that case. What about your
equations? Can they handle that case? Show us that your equations
can handle that case James.

rossum



James Harris

.

Relevant Pages

  • Re: JSH: Mystery increases
    ... solution to the factoring problem. ... many or all of the factor pairs of D-1. ... So just ask yourself why posters have to present their own equations ... correct equations are James. ...
    (sci.math)
  • Re: JSH: Remarkably odd
    ... factoring problem. ... That is not rocket science James. ... I've argued about it a bit and watched in amazement as posters have ... I find it remarkably odd that you refuse to use your method to factor ...
    (sci.math)
  • Re: JSH: Mystery increases
    ... Any solution to the factoring problem has ... stepped up in a huge way, but remarkably posters who have argued with ... Your work contains too many errors James. ... to be interested in mathematics. ...
    (sci.math)
  • Re: Finding large primes, quickly
    ... My mistake, apologies to James. ... posters have a field day. ... Kind of why politics in other areas disintegrates so rapidly, ... Almost every one of your posts has political ...
    (sci.math)
  • Re: warning to those posting pics here
    ... The person who owns the photo didn't give permission for "james" to use it, ... This is directed directly at Lyn who has for some reason decided it is ok to use verbal abuse towards me. ... There is a thief amongst us who likes to steal other posters pics and post them as their own. ...
    (rec.food.cooking)
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