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From: JSH on 10 Nov 2009 19:27
On Nov 10, 11:03 am, Enrico <ungerne...(a)aol.com> wrote:
> On Nov 10, 11:04 am, rossum <rossu...(a)coldmail.com> wrote:
>
>
>
>
>
> > On Tue, 10 Nov 2009 07:23:43 -0800 (PST), JSH <jst...(a)gmail.com>
> > wrote:
>
> > >Enrico just had problems.  I DID find the answer using my approach but
> > >further out than I'd like which made me wonder about the probability
> > >that I've said is associated with it.
>
> > Why did you have to wonder James?  Could it be that you just tried
> > your method on a couple of small examples and thought that it looked
> > as if the probability was about 50% without actually checking on
> > enough examples to be sure?  
>
> > >But it IS a probabilistic approach yet I don't want to use that
> > >to ignore surprisingly bad outcomes.
>
> > Then you need to test it over a wide range of values and actually see
> > what probability you get.  What results do you get from testing it on
> > 50,000 values in the range 10,000 to 2,000,000 for example?
>
> > >What amazes me is how giddy people like you clearly get with even the
> > >hint that I'm wrong versus wishing that someone, anyone, would find
> > >something new and interesting.
>
> > What amazes us James is that you claim such immense importance for
> > results that you have obviously spent all of five minutes checking.
> > We know from previous experience that your initial version of anything
> > is almost certain to have errors in it; that has been the case for as
> > long as I have been following your work.  You have cried "wolf" a
> > great many times, only to say "Whoops, I found a mistake."
>
> > >So ONE LITTLE appearance of an issue and you're stomping and shouting
> > >and hollering with glee.
>
> > Because it was you who were stomping and shouting and hollering with
> > glee because you had solved the factoring problem and how we were all
> > going to have to appear before the SCotUS to justify ourselves.  You
> > holler at us and we will holler straight back.  You are reaping what
> > you sowed earlier James.
>
> > >But the method worked.  It's actually a bit scarier now as there is
> > >increasing evidence that it is actually is a valid approach.
>
> > No James.  Your method finds a solution, but it finds that solution no
> > faster than existing methods.  Speed is of the essence James.  We
> > already have plenty of slow solutions; we are now looking for fast
> > solutions.  You have not shown that your latest solution is fast.
>
> > rossum
>
> > >James Harris- Hide quoted text -
>
> > - Show quoted text -
>
> ====================================================
>
> One thing still missing from James' method is how j is selected.
>
>                                                   Enrico

No, not really. There are size issues as T needs to be roughly equal
to N^2 for 50% probability with a=1, which I knew from the surrogate
factoring research, but kind of forgot.

You should have seen that in your results where as N gets bigger it
takes longer and longer to get an answer, kind of like there are zones
where you CANNOT get the answer, as there are zones where answers are
far less likely.


James Harris

From: Enrico on 10 Nov 2009 20:56
On Nov 10, 5:27 pm, JSH <jst...(a)gmail.com> wrote:
> On Nov 10, 11:03 am, Enrico <ungerne...(a)aol.com> wrote:
>
>
>
>
>
> > On Nov 10, 11:04 am, rossum <rossu...(a)coldmail.com> wrote:
>
> > > On Tue, 10 Nov 2009 07:23:43 -0800 (PST), JSH <jst...(a)gmail.com>
> > > wrote:
>
> > > >Enrico just had problems.  I DID find the answer using my approach but
> > > >further out than I'd like which made me wonder about the probability
> > > >that I've said is associated with it.
>
> > > Why did you have to wonder James?  Could it be that you just tried
> > > your method on a couple of small examples and thought that it looked
> > > as if the probability was about 50% without actually checking on
> > > enough examples to be sure?  
>
> > > >But it IS a probabilistic approach yet I don't want to use that
> > > >to ignore surprisingly bad outcomes.
>
> > > Then you need to test it over a wide range of values and actually see
> > > what probability you get.  What results do you get from testing it on
> > > 50,000 values in the range 10,000 to 2,000,000 for example?
>
> > > >What amazes me is how giddy people like you clearly get with even the
> > > >hint that I'm wrong versus wishing that someone, anyone, would find
> > > >something new and interesting.
>
> > > What amazes us James is that you claim such immense importance for
> > > results that you have obviously spent all of five minutes checking.
> > > We know from previous experience that your initial version of anything
> > > is almost certain to have errors in it; that has been the case for as
> > > long as I have been following your work.  You have cried "wolf" a
> > > great many times, only to say "Whoops, I found a mistake."
>
> > > >So ONE LITTLE appearance of an issue and you're stomping and shouting
> > > >and hollering with glee.
>
> > > Because it was you who were stomping and shouting and hollering with
> > > glee because you had solved the factoring problem and how we were all
> > > going to have to appear before the SCotUS to justify ourselves.  You
> > > holler at us and we will holler straight back.  You are reaping what
> > > you sowed earlier James.
>
> > > >But the method worked.  It's actually a bit scarier now as there is
> > > >increasing evidence that it is actually is a valid approach.
>
> > > No James.  Your method finds a solution, but it finds that solution no
> > > faster than existing methods.  Speed is of the essence James.  We
> > > already have plenty of slow solutions; we are now looking for fast
> > > solutions.  You have not shown that your latest solution is fast.
>
> > > rossum
>
> > > >James Harris- Hide quoted text -
>
> > > - Show quoted text -
>
> > ====================================================
>
> > One thing still missing from James' method is how j is selected.
>
> >                                                   Enrico
>
> No, not really.  There are size issues as T needs to be roughly equal
> to N^2 for 50% probability with a=1, which I knew from the surrogate
> factoring research, but kind of forgot.
>
> You should have seen that in your results where as N gets bigger it
> takes longer and longer to get an answer, kind of like there are zones
> where you CANNOT get the answer, as there are zones where answers are
> far less likely.
>
> James Harris- Hide quoted text -
>
> - Show quoted text -

======================================================

>
> You should have seen that in your results where as N gets bigger it
> takes longer and longer to get an answer, kind of like there are zones
> where you CANNOT get the answer, as there are zones where answers are
> far less likely.
>

What I see in my results are pairs of periodic impulse functions of
periods
equal to the pairs of primes in N. Intersections of the two functions
show
where solutions exist and the whole thing has a period of N, plus
reflection symmetry

In your solution yesterday for X^2 = 2 mod 161, you used
f1 = 143 and j = 111

143 divides 2q + jN evenly ONLY at the places where both
a solution to X^2 = 2 mod 161 and a factorization of 161 exist.
(Your right - it looks elegant)
There are 4 such places at intervals of 161.
Of any such group of 4, only 2 give nontrivial factorizations.

I assume thats the source of your 50% probability claim.

Is it significant that f1 = 143 is itself a solution to X^2 = 2 mod
161 ?

Is it significant that j = 111 is related to another solution of X^2
= 2 mod 161:
X = 74 via 74 * 3 / 2 = 111 ?


Evil, Lying Mathematicians want to know


Enrico
From: amzoti on 11 Nov 2009 20:00
On Nov 10, 4:27 pm, JSH <jst...(a)gmail.com> wrote:

>
> You should have seen that in your results where as N gets bigger it
> takes longer and longer to get an answer, kind of like there are zones
> where you CANNOT get the answer, as there are zones where answers are
> far less likely.
>
> James Harris

What twilight 'zone' do you exist in where anyone accepts this
nonsensical gibberish?

Are you delusional?

You are totally zoned in on the women and don't want to do the math.

Shame on you!
From: JSH on 11 Nov 2009 22:07
On Nov 10, 5:56 pm, Enrico <ungerne...(a)aol.com> wrote:
> On Nov 10, 5:27 pm, JSH <jst...(a)gmail.com> wrote:
>
>
>
>
>
> > On Nov 10, 11:03 am, Enrico <ungerne...(a)aol.com> wrote:
>
> > > On Nov 10, 11:04 am, rossum <rossu...(a)coldmail.com> wrote:
>
> > > > On Tue, 10 Nov 2009 07:23:43 -0800 (PST), JSH <jst...(a)gmail.com>
> > > > wrote:
>
> > > > >Enrico just had problems.  I DID find the answer using my approach but
> > > > >further out than I'd like which made me wonder about the probability
> > > > >that I've said is associated with it.
>
> > > > Why did you have to wonder James?  Could it be that you just tried
> > > > your method on a couple of small examples and thought that it looked
> > > > as if the probability was about 50% without actually checking on
> > > > enough examples to be sure?  
>
> > > > >But it IS a probabilistic approach yet I don't want to use that
> > > > >to ignore surprisingly bad outcomes.
>
> > > > Then you need to test it over a wide range of values and actually see
> > > > what probability you get.  What results do you get from testing it on
> > > > 50,000 values in the range 10,000 to 2,000,000 for example?
>
> > > > >What amazes me is how giddy people like you clearly get with even the
> > > > >hint that I'm wrong versus wishing that someone, anyone, would find
> > > > >something new and interesting.
>
> > > > What amazes us James is that you claim such immense importance for
> > > > results that you have obviously spent all of five minutes checking.
> > > > We know from previous experience that your initial version of anything
> > > > is almost certain to have errors in it; that has been the case for as
> > > > long as I have been following your work.  You have cried "wolf" a
> > > > great many times, only to say "Whoops, I found a mistake."
>
> > > > >So ONE LITTLE appearance of an issue and you're stomping and shouting
> > > > >and hollering with glee.
>
> > > > Because it was you who were stomping and shouting and hollering with
> > > > glee because you had solved the factoring problem and how we were all
> > > > going to have to appear before the SCotUS to justify ourselves.  You
> > > > holler at us and we will holler straight back.  You are reaping what
> > > > you sowed earlier James.
>
> > > > >But the method worked.  It's actually a bit scarier now as there is
> > > > >increasing evidence that it is actually is a valid approach.
>
> > > > No James.  Your method finds a solution, but it finds that solution no
> > > > faster than existing methods.  Speed is of the essence James.  We
> > > > already have plenty of slow solutions; we are now looking for fast
> > > > solutions.  You have not shown that your latest solution is fast.
>
> > > > rossum
>
> > > > >James Harris- Hide quoted text -
>
> > > > - Show quoted text -
>
> > > ====================================================
>
> > > One thing still missing from James' method is how j is selected.
>
> > >                                                   Enrico
>
> > No, not really.  There are size issues as T needs to be roughly equal
> > to N^2 for 50% probability with a=1, which I knew from the surrogate
> > factoring research, but kind of forgot.
>
> > You should have seen that in your results where as N gets bigger it
> > takes longer and longer to get an answer, kind of like there are zones
> > where you CANNOT get the answer, as there are zones where answers are
> > far less likely.
>
> > James Harris- Hide quoted text -
>
> > - Show quoted text -
>
> ======================================================
>
>
>
> > You should have seen that in your results where as N gets bigger it
> > takes longer and longer to get an answer, kind of like there are zones
> > where you CANNOT get the answer, as there are zones where answers are
> > far less likely.
>
> What I see in my results are pairs of periodic impulse functions of
> periods
> equal to the pairs of primes in N. Intersections of the two functions
> show
> where solutions exist and the whole thing has a period of N, plus
> reflection symmetry
>
> In your solution yesterday for X^2 = 2 mod 161, you used
> f1 = 143 and j = 111
>
> 143 divides 2q + jN evenly ONLY at the places where both
> a solution to X^2 = 2 mod 161 and a factorization of 161 exist.
> (Your right - it looks elegant)
> There are 4 such places at intervals of 161.
> Of any such group of 4, only 2 give nontrivial factorizations.

I worked backwards using f_1 = 3 mod 7 and f_1 = 5 mod 23, which gives
f_1 = 143 mod 161.

> I assume thats the source of your 50% probability claim.

That seems more and more to me like a guess having to do with
quadratic residues being so significant.

But I'm looking back over a year and it all gets fuzzy. My past self
seemed to think that was the probability, but I'm not really sure any
more why.

> Is it significant that f1 = 143 is itself a solution to X^2 = 2 mod
> 161 ?

Two key underlying surrogate factoring equations are:

f_1 = ak mod p, and f_2 = a^{-1}(1 + a^2)k mod p

where with N, p is a prime factor of N, and those equations are not
necessarily valid for N, but still end up being valid for some prime
factor of it. I've been using a=1, so if they are valid for both,
then yeah, k will equal f_1, and for the prime case you'd see that is
always the case.

Using k = 3^{-1}(f_1 + f_2) mod N, though works regardless though it's
true mod p, as well, of course. I thought that was cool as I just
jumped to mod N from mod p, and it's not always true that everything
carries over.

> Is it significant that j = 111 is related to another solution of  X^2
> = 2 mod 161:
> X = 74 via 74 * 3 / 2 = 111 ?

I don't know. These surrogate factoring equations can be interesting
to unravel as you're always dealing with two factorizations.

Your pulling information out of one from the other or vice versa so
there are all these underlying mathematical relationships where they
connect to each other.

>                                Evil, Lying Mathematicians want to know
>
>                                Enrico

Hey, to me it's interesting mathematics and easily qualifies as of
interest for "pure math" reasons which I toss out because there are
posters who keep taunting about factoring a large number.

But the underlying mathematics is really this connection between TWO
factorizations, so who knows what you might see playing with it
enough. I suspect some of what you might see would look like
interference patterns.

IN any event, success with a=1 depends no certain things. You might
find more success with a=2. Also T can be even or odd. I often use
odd T, just because. (I kind of don't like messing with a lot of
factors of 2.)

I'm guessing now for various reasons that the probability of success
with a>1 is roughly: ((a-1)/a)*(50%).

With a=1, I'm guessing you have 50% probability with T>N^2, but it
still may work with smaller T but I'm not sure what the probability is
(lots of competing factors come into play).


James Harris
From: Chris McDonald on 11 Nov 2009 23:39
JSH <jstevh(a)gmail.com> writes:

>I'm guessing now for various reasons that the probability of success
>with a>1 is roughly: ((a-1)/a)*(50%).

>With a=1, I'm guessing you have 50% probability with T>N^2, but it
>still may work with smaller T but I'm not sure what the probability is
>(lots of competing factors come into play).


This may be a significant result, worthy of investigation.
I postulate that for any positive integer, 50% to be an upper-bound on
the probability of it being prime, and thus a possible prime factor from
James' factorization techniques. It's amazing.

--
Chris.
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