Re: JSH: Not obvious? Simple math test.

On Jan 16, 7:50 pm, JSH <jst...@xxxxxxxxx> wrote:
On Jan 16, 5:50 pm, "biggus" <dd...@xxxxxxxxx> wrote:



"JSH" <jst...@xxxxxxxxx> wrote in message

news:ee161b52-0d01-4883-8bcc-11bcb3991616@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

On Jan 14, 11:44 am, rossum <rossu...@xxxxxxxxxxxx> wrote:
On Sun, 13 Jan 2008 17:42:48 -0800 (PST), JSH <jst...@xxxxxxxxx>
wrote:

On Jan 13, 12:58 pm, rossum <rossu...@xxxxxxxxxxxx> wrote:
On Fri, 11 Jan 2008 16:41:10 -0800 (PST), JSH <jst...@xxxxxxxxx>
[snip]

Sounds good. Have fun.

Question for James:

At step 6, if I find that k is not coprime to nT, do I stick with the
same value of alpha and step n (= "go to step 3") or do I give up on
that alpha and move to the next value (= "increment alpha by 1 and go
to step 2")? Currently I am doing the latter.

Shouldn't matter. It just will not work at all if k is not coprime to
nT.

When I was coding it up I decided that the first option was easier so
I built my code that way.

Having coded it I ran mu usual tests:

As I have done previously, I tested James' latest factoring method on
500 random composite odd numbers that are multiples of two different
primes, each in the range 500 to 1000. The results are compared to
Fermat's method, trial factorisation (both forward and reverse) and
random picking.

JSH Results

Fermat average = 8.14 probes.
JSH average = 666.74 probes.
Probe ratio = 1 : 81.889
Trial average = 119.67 probes.
Reverse average = 12.57 probes.
Random average = 737.48 probes.
500 trials, 0 misfactors found.

Average alphas tried per factorisation: 84.812
Average n's tried per factorisation: 195.066

I also ran a second test of a modified version which did not include
the four GCDs with "-p" in them. This meant that there were only four
GCDs evaluated for each allowed combination of alpha, n, k and p where
the unmodified version had eight GCDs. Overall this change reduced
the number of GCDs (= probes) but increased the number of alphas
tried.

JSH Results - omitting the four "-p" GCDs

Fermat average = 7.52 probes.
JSH average = 480.14 probes.
Probe ratio = 1 : 63.831
Trial average = 120.48 probes.
Reverse average = 12.11 probes.
Random average = 748.97 probes.
500 trials, 0 misfactors found.

Average alphas tried per factorisation: 121.374
Average n's tried per factorisation: 279.416

As is usual with James' methods it will factorise the target number,
but has no speed advantage over existing methods.

rossum

Surprise, surprise...NOT.

In fact JSH is 60 times WORSE than Fermat, another bad idea down the
drain.

The results had to be bogus. I suspect he just made up the numbers.

___JSH


This is despicable. You have no justification for saying this.
Rossum has
been consistently honest and open in his replies to you, and
remarkably
patient. You will say he must be wrong because you have a "proof".
Your
"proof" however does not include an estimate of how many probes you
need to arrive
at a factorization. Do not try to invoke your old bogus "50%"
argument - that
was discredited many months ago. Your track record in "proofs" is
abominable,
far worse than Rossum's track record in estimating the efficiency of
your
methods relative to Fermat's. Yet here you have the gall to
sneeringly claim
he "just made up the numbers". Far more likely: you just made up the
claim
that you have a proof.

If you were right, you could easily prove Rossum wrong by writing
your
own program (and posting it here) which presents statistics in the
same way
his does. The fact that you have not done so is a big fat clue to
everyone
here, even if they have no understanding of the math. Instead you
accuse
Rossum of just making up the numbers. This is contemptible
behavior.

The truth is, you have yet again devised a method which selects
trial
divisors very inefficiently, and you have yet again deluded yourself
into thinking
your choices have a useful connection to factors of your target.
There are
methods based on quadratic residues - e.g., Gauss's method - but they
make much more intelligent, logical use of the information in those
residues
than your method does, which is why they are the basis for some of
the
more efficient methods of factorization.

Marcus.
.