Re: JSH: Mystery increases

On Sat, 28 Feb 2009 15:55:17 -0800 (PST), JSH <jstevh@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
general you need to know all the factors of D-1 which is slower than
just finding a single factor pair of D.


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.


That means that once you loop through all combinations of factors you
MUST non-trivially factor D.
Tim Smith has posted a couterexample in this thread for the case D=15.
Either your proof has an error or his counterexample has an error.
Can you show us the error in his counterexample?


So it is a direct factoring method--the first in human history as it
only nominally involves search with the looping through of
combinations of factors of D-1.

There are two easy ways to prove that a method is fast.  One is to do
a big-O analysis of the algorithm and show that the algorithm is
faster than existing algorithms.  The other is to actually factor a
large (say 200 bit) number quickly.

Direct solutions can be trickier to push through the usual systems.
Here some might bring up as an issue factoring D-1, and then there is
the issue of combinations. For instance if D-1 = 2p where p is a
large prime, then of course that is going to go a lot faster than if
D-1 has a lot of prime factors.
We need to know how much faster James. Your method is no good if the
only numbers it can factor quickly are of the form 2p + 1. Users of
RSA will simply avoid numbers of that form.


However, my own guess at this time based on how the mathematics
appears is that a factoring algorithm based on the research will be
capable of factoring any number of arbitrary size faster than it can
be used in RSA encryption, ending RSA as a viable option.
You need proof James, not a "guess". You need to show us proof that
your method is fast. In the absence of some proof of speed your guess
is as good as ours.


Unless and until you have done either of these then your proof is
incomplete.  Your method may well find factors, but so does trial
division.  There is nothing you have produced to prove that your
method is any faster than trial division.  Speed is of the essence

Nonsensical given the actual mathematics.

The mathematics links factoring D to factoring D-1. It stands to
reason that it is going to be very, very, very fast when fully
implemented, as in a sense, you're factoring D BY factoring D-1.

here James, and none of your work has any relation to the speed at
which your algorithm will factor a large number.

I disagree.

After all, it is the factoring problem.

Crucial to me was getting help and it looks like one poster has
stepped up in a huge way, but remarkably posters who have argued with
me are acting almost as if that thread is invisible.

We were asked not to post to that thread, and I for one am respecting
that request.  I am certainly reading the thread with interest.



I have YEARS of having had major mathematical discoveries and learned
a long time ago that proof wasn't enough to convince people in the
mathematical community, but I didn't realize just how bad it truly is.

Your work contains too many errors James.  Where you are correct, as

Errors are part of the process of learning. One must crawl before one
can walk.
All of us can make errors.


with your Prime Counting function, most people here are prepared to
agree that it is correct.  Where you work is incorrect, as with all
previous iterations of your "solution" to the factoring problem, then
your errors are pointed out to you.  You have cried "wolf" so many
times now that many people are very skeptical of what you say.  Your
reputation precedes you.

Mathematical proof is not about reputation. It is about proof.
People are about reputation. I have tested at least half a dozen of
your previous claimed solutions to the factoring problem. All of
them, without exception, found factors. All of them, without
exception, were too slow to be of any interest. So far my testing on
the early versions of your current idea have shown the same thing,
your method finds factors but it finds them too slowly. That is why I
am emphasising the need to show how fast your latest method is. Speed
was the Achilles' heel of all of your previous attempts.

You say that you are brainstorming. Part of brainstorming is to
listen to the feedback to see where your ideas can be improved. I am
giving you exactly that feedback - you MUST look at how fast your
algorithm runs in practice.


The mystery here is about denial of proof.
We have seen errors in your claimed proof so it is not a proof, just a
claim of one. A proof of a solution to the factoring problem MUST
include a proof of the speed of the algorithm. No proof of speed
means no solution to the factoring problem.

Better look at something on big-O James or get coding.

rossum

[snip]


James Harris

.

Relevant Pages

  • Re: Factoring problem, solved
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  • Re: Factoring problem, solved
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    (sci.crypt)
  • Re: Proof factoring solution is closed form
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    (sci.math)
  • Re: Proof factoring solution is closed form
    ... >> your proliferation of redundant threads that you don't pay attention ... Remember I'm the inventor of surrogate factoring. ... But are you implying that if Rick were the inventor, ... > the factoring problem as there was every reason to believe that I would ...
    (sci.crypt)
  • Re: Coding opportunity with factoring problem solution with Fermat numbers
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