Re: JSH: Contradictory behavior, issue of math fraud

[JSH]
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?

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

[JSH]
I asked, what if?

[Mas Plak]
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.

[rossum]
Not always.

Be a little careful here, lest Jimmy leap to (yet another :-( ) wrong
conclusion. Because his "methods" always have strange convolutions, "a
probe" in a JSH method is typically a lot slower than "a probe" in the
random-gcd algorithm. For example, random-gcd kicks out candidates just
as fast as random (or pseudo-random) numbers can be generated, while
James usually has you /in addition/ putzing around with systematically
generating all two-integer factorizations of some other number too.

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.

James will never understand this, but "Mas Plak" may: James guesses at
method after method that /essentially/ feed pseudo-random integers into
a gcd calculation. But viewed as pseudo-random generators, they're of
poor quality, so an effective way to improve their "performance" has
always been for me to treat them /as/ nothing more than PRNGs, and make
simple changes that improve the coverage of the pseduo-random candidates
generated. Since the number of integer factors of an integer (the
surrogate S) depends on the /powers/ of the primes in S's prime
factorization, artificially multiplying S by 2^3 * 3^3 * 5^3 first can
greatly boost the number of candidate pairs generated, and without
making S itself any harder to factor.

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

Nevertheless, I bet it was still much slower (by clock time) than plain
old random-gcd.
.

Relevant Pages

  • Re: JSH: Contradictory behavior, issue of math fraud
    ... but accept the FACT that surrogate factoring is twice as slow as ... James gets the factorisation of S "for free" - I ... Also it is worth mentioning that your count of "probes" potentially ... distort the success of surrogate factoring in the negative, ...
    (sci.math)
  • Re: JSH: Contradictory behavior, issue of math fraud
    ... but accept the FACT that surrogate factoring is twice as slow as ... For example, random-gcd kicks out candidates just as fast as random (or pseudo-random) numbers can be generated, while James usually has you /in addition/ putzing around with systematically generating all two-integer factorizations of some other number too. ... Reverse average = 12.70 probes. ...
    (sci.math)
  • Re: JSH: Latest factoring idea is crap
    ... is good enough for top mathematicians, he's got no reason to try to make it ... Since he's attracted to messy methods involving multiple free choices, ... factoring 35 and show him that it didn't find a factor after all. ... Subject: JSH: Now what? ...
    (sci.math)
  • Re: JSH: Surrogate factoring, periodic behavior
    ... Fermat average = 7.58 probes. ... JSH average = 1635.83 probes. ... His SF is more than 2 times slower than random guessing!!! ...
    (sci.math)
  • Re: Proof factoring solution is closed form
    ... > Whether your approach to factoring leads to anything remains to ... JSH recently even seemed to agree that method doesn't always work. ... reality don't bother you, ya, lots of things are arguably poly-time. ...
    (sci.math)