Re: JSH: Surrogate factoring, periodic behavior

On Sep 1, 3:34 am, rossum <rossu...@xxxxxxxxxxxx> wrote:
On Sat, 01 Sep 2007 05:21:41 -0000, JSH <jst...@xxxxxxxxx> wrote:
Factored trying 5 surrogates on the fifth surrogate using k=1 where
the start was with n=7.

I ran my usual tests again 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.

Fermat average = 7.58 probes.
JSH average = 1635.83 probes.
Probe ratio = 1 : 215.752
Trial average = 118.52 probes.
Reverse average = 12.12 probes.
Random average = 727.79 probes.

500 trials, 0 misfactors found.

Here is output from my program and a run I just did testing out some
new theory.

Here for various reasons I won't explain I'm using k=30, starting with
n=1, and there is a lot wrong with this example from my standpoint as
by my theory I don't think it should have factored at this point.

java Factor 34587541
n_max=0
Number factored.
Total all combinations: 21
Time: 0
Time/combination: 0.0


Surrogate:
( 11^2 )( 13 )( 19 )( 8101 )
Product: 242114587

Surrogate combinations checked:
Initial Factorization:

f_1=307
f_2=112663
Now checking its factors...
Success!
Factors:
( 307 )( 112663 )
Product: 34587541

In coming is 34587541
Factored for k : 3
Not factored for k: 4
Factored fuel percentage: 42%

Factored fuel : 3
Fuel not factored: 4
Factored fuel percentage: 42%

Processing time: 78
Number of digits: 8
bitLength=26

The program I use loops through trying to factor the surrogate and if
it can't fully factor it just keeps on going, where in this case it
says it factored 3 fully and could not fully factor 4, so I guess it
checked 7, but now I'm not sure what.

As it looks like to me it only tried one surrogate, so I'm not sure
why it says it checked seven unless, um, the code is doing something
I'm not sure about which wouldn't be a surprise.

I'm kind of half-heartedly hacking at it because I think it stupid
that the world should suffer because you people lie.

How is that fair?

In any event, it's an example of what I mean of the kind of behavior I
see all the time with dinky numbers.

Totally not random.

Average k's tried per factorisation: 1.000
Average n's tried per factorisation: 47.040

k was fixed at 1 and n was 7, 8, 9, ...

Part of the problem I've run into with comments about surrogate
factoring have been repeated claims it works only as good as trial
division, but hey, I programmed the damn thing.

Any chance of seeing your code?


No.

But you know I'm rather fascinated by this entire process as it
reminds me of when I was working on prime counting, and eventually
posters just went to lying about my research.

But this time if I figure out what's going on I can just factor big
numbers, and see if you try to lie your way out of that, which makes
the situation different.

Your only hope is that I'm bluffing.

Ok, I'm bluffing. Sleep ok tonite.

That's my present to you.


James Harris

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