Re: JSH: Surrogate Factoring Paper Accepted!

On 14 Dez., 22:01, "JSH" <dd...@xxxxxxxxx> wrote:
Oh well, enough bravado on my part as I'm not certain this will work
and waiting for it just seems silly. The Bulletin of the AMS
did reject. Why would they change their minds between now and then?

The expert opinion is noted. Here is what my research says, which
presumably then will not work, but I do not know why it would not.

So I submitted it tohttp://math.rejecta.org/about-rejecta-mathematica
and they have accepted my paper for publication!

Given a target composite T, from theory using x^2 = y^2 mod T and k =
2x mod T, it can be proven that

(x+k)^2 = y^2 + 2k^2 mod T

must be true for any solution of a difference of squares.

Explicitly to solve you need solutions for

(x+k)^2 = y^2 + 2k^2 + nT.

The algorithm picks x directly, choosing x = floor(sqrt(T)), so k =
2x, and then ranges for the n's from

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

and

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

which with my program has meant roughly 32 surrogates to factor.

By the theory, if you can fully factor all 32 surrogates for any
target T, then you will non-trivially factor T.

If you cannot factor all 32 with the given x, you can increment it by
1 and try again, indefinitely.

Note that you can also use x = floor(sqrt(2T)) to have about 64
surrogates and much greater odds but I'm not clear how that works
exactly and besides if you can factor 32 with the first one then you
have the target in hand.

It is so weirdly simple and I think the theory is correct, but I guess
mathematicians are supressing me and call me wrong.

I have tried to implement with my own programs but as I pointed out in
a previous post, I use recursion and with big numbers fewer and fewer
of the surrogates get factored, so it craps out.

I am confident that I can work that problem out so what I said
earlier was bravado on my part.

James Harris

A quote from the rejecta rules shows that the real JSH cannot
be expected to succedd in submittin a paper there:


As an author, you are generally expected to address two main points in
your open letter:

* Discuss the original review process, including the apparent
reason for the paper's rejection.
* State the case (in spite of the rejection) for the paper's value
to the mathematical community.

Additionally, you must reveal:

* any known errors in the paper (or accidental rederivations of
earlier work)
* any changes you have made since the paper was previously
rejected (though making such changes is not required)
.

Relevant Pages

  • Re: JSH: SF Algorithm
    ... you have provided no rationale for having a high probability ... have the target in hand. ... of the surrogates get factored, ... That should be a manageable technical problem. ...
    (sci.math)
  • Re: JSH: SF Algorithm
    ... Bulletin of the AMS ... Why would they change their minds ... which with my program has meant roughly 32 surrogates ... have the target in hand. ...
    (sci.math)
  • JSH: Surrogate Factoring Paper Accepted!
    ... enough bravado on my part as I'm not certain this will work ... The Bulletin of the AMS ... which with my program has meant roughly 32 surrogates to factor. ... have the target in hand. ...
    (sci.math)
  • Re: JSH: SF Algorithm
    ... Why would they change their minds between now and then? ... The expert opinion is noted. ... which with my program has meant roughly 32 surrogates to factor. ... have the target in hand. ...
    (sci.math)
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