Re: JSH: Now we're golden!

On Jan 19, 4:04 pm, JSH <jst...@xxxxxxxxx> wrote:
Wow! The poster Enrico noticed cases where my factoring congruences
weren't working, and I was able to work out yet another fascinating
feature, as well as explain something that might have been missed up
until now which is that you get one 'a' and k pair for each unique
factorization.

So, yes, now it's mathematically proven that I found a solution to the
factoring problem, and I want to definitely thank Enrico and would
like to give him mention in the paper.

I will say now that an early draft of the paper is at the Annals of
Mathematics, but I ended up sending two revisions after I rushed them
my early research and have thankfully sat for a while as I worked out
the issues.

There is no doubt I'd think that a paper solving the factoring problem
deserves publication in the Annals.

Some of you may have tested out the congruences and found they did not
always work, which gave you doubts, but now the answer is that there
is a quirk of prime numbers, as there are two basic types: those for
which the negative of the quadratic residue is a quadratic residue and
those for which it is not.

So, for instance, with p=17, Enrico noticed that the congruence
relations would not work to non-trivially factor 15. I dove into the
underlying equations and found that they would not work, and figured
out the answer as to why.

It helped that I had the existence equation for 'a' handy.

Rather wild though. All integer factorizations are controlled by the
factoring congruences, but some primes exclude themselves but only if
they are the primes for which the negative of their quadratic residue
is a quadratic residue.

My celebration should be somewhat muted though as it is now definite
that the factoring problem is SOLVED.

Governments around the world and institutions affected should behave
accordingly.

I am directing EMC2 to give a press release as soon as possible on the
situation through its RSA division.

James Harris

First!

--
THE Troll Feeder

Beating other troll feeders to the trowel since 2008.
.

Relevant Pages

  • Re: JSH: Now were golden!
    ... There is no doubt I'd think that a paper solving the factoring problem ... which the negative of the quadratic residue is a quadratic residue and ... but some primes exclude themselves but only if ... they are the primes for which the negative of their quadratic residue ...
    (sci.crypt)
  • JSH: Situation has changed
    ... but I want to emphasize to the physics ... composites that are 9 mod 11 that are less than T, ... And that's the high level explanation for why the factoring problem ... This technique can tackle numbers easily up to 143!, using primes from ...
    (sci.physics)
  • Re: JSH: Situation has changed
    ... And that's the high level explanation for why the factoring problem ... This technique can tackle numbers easily up to 143!, using primes from ... shows that the primes TELL something about the composite that you wish ... A physics student could figure this out. ...
    (sci.physics)
  • Re: JSH: What are you people?
    ... primes you might pick, ... It's easy algebra. ... definition of "disconnected with regard to". ... based on your most recent posts in "Solving the factoring problem", ...
    (sci.crypt)
  • JSH: Way too interesting
    ... So I have this neat result using congruences which is so easy and ... trivial that I can just put it out there and watch what happens! ... microscope ever built--a simple solution to the factoring problem ... versus a social view that I'm just some crackpot. ...
    (sci.math)
Quantcast