Re: Issue of triviality, surrogate factoring

From: Larry Hammick (larryhammick_at_OMIT-MEtelus.net)
Date: 04/08/05 

Date: Fri, 08 Apr 2005 04:45:08 GMT

"Proginoskes"
> jst...@msn.com www.crank.net/megalomaniacs.html wrote:
> > Last week I discovered the surrogate factoring theorem which
> > directly links factorizations. You can see the theorem at
> >
> > http://groups-beta.google.com/group/Surrogate-Factoring
> >
> > but I want to discuss how it works in this post in a way that
> > might be easier to understand than if you just look at the
> > theorem itself, as it can look at little complicated so that
> > the abstractions are lost.
> >
> > The surrogate factoring theorem links factorization such that
> > if you have non-zero integers A and B, if you find factors
> > f_1 and f_2 such that
> >
> > f_1 f_2 = B^2(A^2 - B^2)
> >
> > it will give you factors g_1 and g_2 such that
> >
> > g_1 g_2 = A^2(A^2 - B^2)
> >
> > where all the factors are rationals.
>
> Stop right there!
>
> It only seems appropriate that you named this thread "Issue of
> triviality", since that's what rational factors are: Trivial.
>
> If r is any nonzero rational number, and M is an integer (or it could
> even be a rational number, for that matter), r is a rational factor of
> M, as is M / r.
>
> Watch: r * (M / r) = M, no matter what r is.
>
> So I have found ALL rational factors of M: namely ALL nonzero rational
> numbers.
>
> The factoring problem, as the rest of the world defines it, requires
> that r and M / r both be INTEGERS (and both at least 2). That's what
> makes RSA so secure; finding the integer factors of M is INFINITELY
> harder than finding all the rational factors of M, since I've just
> shown you what the rational factors of any rational number are.
>
> RATIONAL factors are TRIVIAL!
>
> Don't start any more threads until this ELEMENTARY fact sinks in.
JSH certainly picked a poor subject on which to
claim to have made a big breakthrough. The RSA
challenge numbers are staring him in the face and
he can do nothing about them. Factorization is
important for reasons having nothing to do with
the academic press; yet the people to whom it
is important (good guys and bad guys alike)
totally ignore James Harris. He'll keep starting
new threads on Usenet because Usenet is all
he's got.

Relevant Pages

  • Re: Issue of triviality, surrogate factoring
    ... > Last week I discovered the surrogate factoring theorem which directly ... > links factorizations. ... > Notice that you have a symmetry and that symmetry is only broken in ...
    (sci.crypt)
  • Re: Issue of triviality, surrogate factoring
    ... >> directly links factorizations. ... >> where all the factors are rationals. ... them out into those two infinities, but that's you, a human being. ...
    (sci.crypt)
  • Issue of triviality, surrogate factoring
    ... Last week I discovered the surrogate factoring theorem which directly ... links factorizations. ... as you can simply switch variables. ...
    (sci.crypt)
  • Re: Issue of triviality, surrogate factoring
    ... > directly links factorizations. ... > where all the factors are rationals. ... triviality", since that's what rational factors are: ...
    (sci.crypt)
  • Re: Issue of triviality, surrogate factoring
    ... > Last week I discovered the surrogate factoring theorem which directly ... > links factorizations. ... both units in the ring of rationals (whether you believe the rationals ... form a ring or not). ...
    (sci.crypt)