Re: Proof factoring solution is closed form

From: Tim Peters (tim.one_at_comcast.net)
Date: 02/10/05 

Date: Thu, 10 Feb 2005 03:04:52 -0500

[JSH]
> ...
> I say, quit hiding things, put up your example where I can see it, like
> in a thread where I'm paying attention, as if you're right I'd like to
> know.

Rick replied in one of the threads you started. How is he supposed to guess
which of those you pay attention to? If you're so bored by your
proliferation of redundant threads that you don't pay attention to them
anymore, and are too lazy to do a simple search, tough luck.

You're probably the only one reading these threads who isn't aware of it. I
verified his results later, and gave more examples of M and j where no
factorization is obtained, despite having the full factorization of -T*j^2
in hand, and cycling through all possible ways of splitting the latter into
a product of two integers.

Now you've steadfastly refused to specify an algorithm, or even give a fully
worked-out example for a composite as small as 15. In addition, your
implementation doesn't work (according to you), so there's no point staring
at that to try to divine what you think either. Consequently, I can't claim
that Rick's very clear derivation actually matches what you think your
method is. Rick made what looked to be an excellent attempt at spelling out
an algorithm based on what you've written, and there's no doubt that the
algorithm he specified fails to find a factor from many <M, j> pairs; and it
appears that as M grows larger, the number of successful j's shrinks (e.g.,
at M=15, all j work; at M=1005973, j=1 didn't work, j=2 didn't work, j=90
didn't work, and j=42603 succeeded 3 times out of 2376 ways of
splitting -T*j^2, a rate no better than picking candidate factors at
random).

If you think that's wrong, do what you should have done at the start:
specify the algorithm you have in mind (a pile of equations isn't an
algorithm -- as a programmer, you shouldn't need to be told that).

BTW, when someone replies in a thread you started, and you call that being
"coy" and "hiding things", you sound insane -- honest.

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