Re: Extraodinary to supposedly ordinary
From: Tim Peters (tim.one_at_comcast.net)
Date: 02/18/05
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Date: Thu, 17 Feb 2005 21:02:30 -0500
[JSH]
[...]
> Now, supposedly, surrogate factoring is just some random, or, <gasp>
> worse than random method for factoring!
My computer experiments suggested that two of your _algorithms_ perform
worse than picking integers k at random in 1..M-1, then seeing whether
gcd(k, M) reveals a factor.
That's not a matter of argument, it's a much simpler matter of running the
algorithm, counting how many gcds it does before it finds a factor, and
comparing that to the number of gcds a random method using a very good
random number generator requires for the same M (I used the Mersenne Twister
here, just because that's what Python ships with). The method requiring the
fewer gcds then wins. Yours lost to random-gcd, over and over and over
again, and I trust my computer to add 1 and compare integers more than I
trust your claims of proof.
I haven't done those experiments on your latest algorithm, by which I mean
the one that searches over splittings of T^3 j^2, and adds 2Tj^2. I don't
intend to spend time on that either, unless you explain first why it doesn't
factor some odd composites that aren't the square of a prime. If you don't,
then I assume your latest proof is also incorrect (beats me -- I can't make
sense of your "proofs"; Rick Decker has pointed at steps he believes are
incorrect, though), in which case you'll come up with some other algorithm.
When you come up with an algorithm that actually works (actually factors
integers that people give to it), then I'll pay attention again.
Here's a simple challenge for you: you claim your latest algorithm should
work. At least three people (including me) have given examples of specific
<M, j> pairs where it fails to find a factor. They weren't trivial
examples, and the latest method can generate an enormous number of gcds, so
they're hard to analyze (either because the integers are huge, or the number
of gcds is in the millions).
So here's a much easier case: my implementation of your latest algorithm
fails to find a factor of M=7387 at j=1. It tries 640 gcds: 632 return 1,
and 8 return 7387. (BTW, if it were picking gcd candidates truly at random,
it would be expected to find a factor of 7387 about 14 times in 640 tries.)
So you show the arithmetic: if your algorithm is correct, show how it
factors M=7387 at j=1. I don't care how that turns out: if you can show
how it factors that, great, it will point out an error in my
implementationm, I'll repair that, and retry the other failing examples I
posted (and I could post many more -- literally millions of failing
examples).
If you can't show how it factors M=7387 at j=1, you have no cause for
complaint here.
...
> You people seem to not know what mathematics is.
Show that you know what arithmetic is <0.1 wink>.
- Next message: cuckookkoo_at_yahoo.com: "Re: GOPAL SARASWAT'S THIRD TERRORIST TACTICS: ASSAULT BY VULGARITY (CCMM with VLMT)"
- Previous message: Yan Zhang: "Re: John Gabriel's Theorem Revisited."
- In reply to: jstevh_at_msn.com: "JSH: Extraodinary to supposedly ordinary"
- Next in thread: David C. Ullrich: "Re: JSH: Extraodinary to supposedly ordinary"
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