Re: JSH: Contradictory behavior, issue of math fraud

On Mon, 3 Sep 2007 15:09:16 -0500, "Mas Plak" <spamless@xxxxxxxxxxxx>
wrote:


"JSH" <jstevh@xxxxxxxxx> wrote in message
news:1188833147.062403.32640@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
On Sep 3, 1:42 am, rossum <rossu...@xxxxxxxxxxxx> wrote:
On Sun, 02 Sep 2007 10:19:32 -0700, JSH <jst...@xxxxxxxxx> wrote:

But if the idea turns out to be a brilliant one which means factoring
is not a hard problem after all, then how can mathematicians who not
only couldn't figure it out, but who ignored it when presented with it
be considered to be true experts in the field?

In its current version surrogate factoring is too slow to be
considered "brilliant". Only when you have speeded it up sufficiently

I asked, what if?

Stick to reality, James, I know it can be hard for you, very hard, but
accept the FACT that surrogate factoring is twice as slow as random
guessing.

TWICE AS SLOW AS RANDOM GUESSING.
Not always. Some of the iterations of James' method are better than
random. For example, with k = 30, n = 7, 8, 9 ... and a suggestion by
Tim Peters of using S = 27000 * (2*k^2 + n*T) then the results are:

Fermat average = 8.35 probes.
JSH average = 608.86 probes.
Probe ratio = 1 : 72.883
Trial average = 118.63 probes.
Reverse average = 12.70 probes.
Random average = 745.43 probes.
500 trials, 0 misfactors found.

Average n's tried per factorisation: 2.430
Average k's tried per n: 1.000

This version is better than random. Tim's reasoning for his
suggestion was that by ensuring a lot of small factors in S, 27000 =
(2 * 3 * 5)^3, each S will generate a lot more factor pairs and so is
more likely to hit a factor of T. The results show that with Tim's
suggestion fewer values of n have to be tried before hitting a factor.

Taking this further, I tried k = 30 with n = 12, 18, 24, 30, ... and I
got James' method down to about 580 probes.

rossum

.

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