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 of information
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 is information wrapped up in the intersection between the
primes.
That information determines 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 that
information out.
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 its information systems.
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 about information theory 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
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