Re: JSH: One other option

On Sep 12, 5:00 pm, JSH <jst...@xxxxxxxxx> wrote:
On Sep 12, 12:01 am, Proginoskes <CCHeck...@xxxxxxxxx> wrote:



On Sep 11, 9:46 pm, JSH <jst...@xxxxxxxxx> wrote:

On Sep 11, 8:17 pm, marcus_b <marcus_bruck...@xxxxxxxxx> wrote:

On Sep 11, 7:19 pm, JSH <jst...@xxxxxxxxx> wrote:
[...]
It turns out Marcus pointed something out in another thread so I can
give a simpler definitive test of the latest theory which oddly takes
away any factoring of surrogates. Thanks Marcus!!!

Why ... I feel so unworthy.

Kind of odd really, but fascinating to contemplate as by the theory
the following algorithm should be applicable against an RSA sized
number factoring it in a maximum of 32 trials:

Note, still with x^2 = y^2 mod T, and k = 2x mod T.

So then, with x = floor(sqrt(T)), k = 2x,

n_min = floor((4(x+k-1) - 2k^2)/T)

and

n_max = floor(((x+k)^2 - 2k^2)/T)

you loop through y = sqrt((x+k)^2 - 2k^2 - nT), with n's from n_min to
n_max, looking for a
perfect square and the theory says there must be at least one,

Let's see. Let T = 77. Then:

x = floor(sqrt(77)) = 8

k = 2x = 16

nmin = floor(-420/77) = -6

nmax = 0.

So now we have the following table:

n (x + k)^2 - 2k^2 - nT
----- ---------------------------
-6 526
-5 449
-4 372
-3 295
-2 218
-1 141
0 64

Only the last of these is a perfect square, and
it yields y = 8. Since x = 8,

x^2 - y^2 = 0 = 0 mod 77,

but of course this gives no useful factors of T.

So over the specified range of n's, none of
the y's is a useful perfect square.

You're right. It seems though that 8 is too small to work as the
theory is setup with the assumption that abs(x)>abs(y).

Try x=9.

Have fun!

Oh yeah, it seems that with dinky numbers you can find these trivial
exceptions near the edges.

What conditions on T are required so that it's not "dinky"?

I wonder why.

If you find that x=9 does not work, then, hey, maybe I need to re-
check the theory!

But you know it will work.

Hmmmm...interesting though that the limits didn't handle that case
with a dinky number.

Something to wonder about....

Something else to wonder about: JSH claims to be a programmer. The
above could EASILY have been coded in any language (even Java). Why
doesn't JSH take the ten minutes necessary to write the program and
run it, seeing that it doesn't work? I mean, all you have is write
something like

Turns out the hypothesis doesn't fly so it doesn't matter.

But yes, I could have easily checked the assertion in a couple of
minutes but did not.

I DID however shoot down a supposed counterexample to the key result I
initially stated before Marcus distracted me with his angle that
proved wrong.

It's mathematical research people.

Whether you believe the truth or not it is research.

I do at times chase down various leads but often I just post them to
have someone else check them.

If you ever do get something that is proven that way, will you give
them credit, as a co-author?

--- Christopher Heckman


.

Relevant Pages

  • beta version of Victor Shoups book, "A Computational Introduction to Number Theory and Algebra&
    ... Computing with Large Integers ... The Basic Euclidean Algorithm ... Factoring and Computing Euler's phi-Function are Equivalent ... The Existence of Finite Fields ...
    (sci.crypt)
  • Re: Ultimate check, new way to factor or not?
    ... It's commonly known as a the "factoring sieve" and Fermat showed that ... It is listed as "algorithm ... "factoring with sieves" on pp.389. ... > when it defies the mathematics. ...
    (sci.crypt)
  • Re: I was right, surrogate factoring proof
    ... primes divide n -- at most I'll have to look through sqrt/ ... But don't forget that's included in the cost of the algorithm! ... if surrogate factoring ever becomes ... two values are congruent modulo p, and hopefully not congruent modulo n/p. ...
    (sci.math)
  • Re: I was right, surrogate factoring proof
    ... primes divide n -- at most I'll have to look through sqrt/ ... But don't forget that's included in the cost of the algorithm! ... if surrogate factoring ever becomes ... two values are congruent modulo p, and hopefully not congruent modulo n/p. ...
    (sci.crypt)
  • Re: More math stuff, truth and social reality
    ... > out that I use brainstorming, where you generate lots of ideas during ... fast as other efficient factoring algorithms. ... I don't see evidence of lying, ... algorithm) is in fact the truth. ...
    (sci.math)
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