Re: JSH: Situation has changed

On Feb 5, 5:31 pm, JSH <jst...@xxxxxxxxx> wrote:
Turns out the factoring problem is not only trivial to solve with
modern computing technology, but it's trivial to explain why, as I
showed in a previous post, but I want to emphasize to the physics
community why that is correct.

If you have T = r_1 mod p_1 where p_1 is some prime and r_1 is some
residue modulo that prime you have a certain amount ofinformation
about the target T.

For instance, if T = 119, then T = 9 mod 11, and there are other
composites that are 9 mod 11 that are less than T, like 20.

But if all you have are residues modulo T, it takes a certain number
to constrain T to one equal to your target or greater, like I
demonstrated in my previous post by using T = 2 mod 13.

T = 9 mod 11 and T = 2 mod 13, force T equal to 119 or greater.

But if you have factors f_1 and f_2 where f_1*f_2 = T, then they are
being constrained as well.

So there isinformationwrapped up in the intersection between the
primes.

Thatinformationdetermines a minimum value for T, so it determines
values for factors of T.

If you know that then you just go looking for how to pull thatinformationout.

And that's the high level explanation for why the factoring problem
can be easily solved.

The actual solution is not that complicated but I think it less
important than explaining HOW you know there must be a simple solution
available.

This technique can tackle numbers easily up to 143!, using primes from
100 to 1000, where to get an understanding how the estimate of primes
needed using m where m is chosen such that T/m! < 1 is such an
overestimate let's go back to T = 119, where only 2 primes were
needed.

With it, m = 5, as 119/5! < 1.

So 143! is a vast underestimate to the size of the composite that can
be tackled by just using the primes from 100 to 1000.

Who knows exactly why mathematicians presented factoring as a hard
problem with which the world could secure itsinformationsystems.

But what you know now if you can understand informational complexity
is that the system can be easily broken if it really is breakable just
by factoring large composites.

Throw out what you know aboutinformationtheory if you want to ignore
these posts and then go back to work doing what you're doing--waiting
for the world to come crashing down around your ears.

But if you do that then you are not a physicist, or not any kind of
physicist that the world needs in what could be one of its most
desperate times.

James Harris

It still is remarkable to me that a simple exercise in considering the
information available tells you that the factoring problem must have
an easy solution.

The example I like the example with T = 9 mod 11 and T = 2 mod 13
constraining you to T = 119 mod 143, where 119 is the target composite
shows that the primes TELL something about the composite that you wish
to factor, and there is information in there that can be exploited.

So if you have a target composite like an RSA public key, you can use
primes to probe the damn thing, with a series of values taken modulo
various primes and just pull the information out of it as to how to
factor it.

And why would the mathematicians not know this?

I think they just don't think like problem solvers in other fields,
and actually LIKE to believe more than prove and they aren't great
experimenters from what I've seen.

In short, I think modern mathematicians are trained wrong.

And the way that is dramatically evident is that they put forward a
system that is being used to protect your information and mine, as
well as millions of people worldwide that can be explained to be
flawed with only a tad bit of information theory.

How you train students can decide how well they think and that
determines what they can discover.

A physics student could figure this out.

Math students might never have.


James Harris
.

Relevant Pages

  • 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: Quantum Gravity 234.2: (Complex or Real) Rational Number Physics
    ... Guess that is another Fundimental set of integers found. ... Or any part of physics? ... From Osher Doctorow: ... the lowest primes in magnitude and primes are the Number Theory ...
    (sci.physics)
  • both Riemann Hypothesis and Twin Primes have no proofs; #139; 2nd ed; Eucl
    ... Twin Primes, and here we have the trouble that it is far more reasonable ... to think they are finite rather than infinite since we have the creation process of higher even n-tuple-primes. ... Finite, and beyond finite is Incognitum, and beyond Incognitum is ... it since that is where Physics ends and since math is only a subset of physics, any further pondering is just dreamlike imagination. ...
    (sci.math)
  • Quantum Gravity 155.3: Generalization to Primes and Quantum Hamiltonians by H. C. Rosu
    ... on physical applications of the Riccati Differential Equation have ... Rosu's paper isn't about perfect primes or perfect numbers or Mersenne ... both primes and physics and perfect numbers and physics. ...
    (sci.physics)
  • Re: Cantorian pseudomathematics
    ... > It's a direct and easy consequence of Euclid's method of proof. ... > that he showed that for any set of primes, ... You must really rid yourself of the idea that mathematics is only ... has really *nothing* to do with physics. ...
    (sci.math)