Re: What surrogate factoring theory now says

On Mar 20, 11:25�pm, "Nomen Lapetos" <nos...@xxxxxxxxxx> wrote:
"Enrico" <ungerne...@xxxxxxx> wrote in message

news:1174448963.111354.193940@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
On Mar 20, 7:36?pm, jst...@xxxxxxxxx wrote:





I want to emphasize that there can be a new factoring method that just
takes a while to be fully engineered, as there is the theory and there
is the engineering into a practical solution.

Like Isaac Newton knew difference of squares, but he didn't have the
Number Field Sieve.

Surrogate factoring theory says that you can turn factoring a hard
target T, into a problem of factoring an indefinite number of
surrogates S_1, S_2, S_3, ... making the problem potentially
tractable.

My own target for my research is factoring an RSA sized number--of any
bit length feasible--within ten minutes on a home computer.

That has been my research target for years now. The theory says that
once the engineering is figured out that is achievable.

You can personally check the very simple underlying mathematics
yourself.

(Web search on surrogate factoring, stay away from the old failed
stuff though.)

Mainly I just added one more congruence to the difference of squares.

So it's not like the algebra is hard, or it's difficult to follow.

But just like with just the difference of squares, figuring out a
practical solution could take a while, where I don't think it'll take
centuries like with difference of squares to the NFS.

I am in the process of trying to turn what could take years of
research from lots of people around the world into months or days of
research where I am the primary engine, but I could fail, and others
could succeed.

So, say, Russia could succeed. Or China could succeed. Or Iran could
succeed. Or, maybe even North Korea could succeed.

Would my own country the United States?

Sure, but history says that people here might not bother because we're
on the top of the heap.

People at the top tend to ignore "crackpot" ideas.

But I could be wrong, right? Lots of math people say I'm a crackpot
and I've been babbling about surrogate factoring for YEARS, including
in the past having said that I'd solved the factoring problem, when I
hadn't.

Yup. I've failed a lot. I admit it. But I've succeeded a lot, and
"mathematicians" won't admit it.

Roll the dice and the fate of the world could change.

That's how it's happened before...people like you under-rate the power
of ideas despite thinking you're idea people, and you ignore something
you DECIDE is dinky and worthless, and civilization itself changes.

If that didn't happen, no dominant country would ever lose that
position. We might be under the Persian Empire, or the Roman or the
Egyptian or some other if people just learned not to underestimate the
power of ideas.

Then again, I could be wrong. I don't think I am, but I have been
wrong before.

But hey, it's mathematics!!! I say, don't trust me. I don't trust
you, or I wouldn't be making this post. I think most of you are
complacent idiots who would let the world go up in flames because
you're too small-minded and maybe corrupt to really care, and I don't
trust you.

Go with the math.

If I'm right, it says I'm right. If I'm wrong, it says I'm wrong.

If it says I'm right, and you think you can just play the odds that no
one in the world will figure this out, not Russia, not China, not
anybody, and you're wrong...well, welcome then to a Brave New World,
and yet another example that history repeats...

James Harris

Hey, James!
You don't have to factor each surrogate from scratch.
If prime P divides 2k^2 + wT then
prime P also divides 2(k+PX)^2 + (w + PY)T
where X, Y are any integers.

This shows up best on Excel with k varying on the horizontal
and w varying on the vertical - each surrogate is calculated
at the intersection and its value mod P is taken with
conditional formatting used to highlight the 0 values.

Any P by P region will tesselate the whole plane, so its easy
to set up a sieve to strain out the small primes.

                                  Enrico

**got an example you could attach, or post in text?- Hide quoted text -

- Show quoted text -

I checked a text paste - no good. Line wrap and no color coding
makes the example useless.

I don't know how to attach an excel file to a reply, and since
I'm using an excel extension for big numbers, I don't think
the attachment would work when you received it.

How are you at Excel? I suppose I could provide directions
to set up an example ***. The trick is to use named ranges
for the w and k variables, pick any T you like, then at each
cell, calculate (2*k^2 + wT) mod some small number like 5, 6, 7
and use conditional formatting on each cell to highlight zero
values. If your *** is bigger than twice the modulus chosen,
the periodicity in both directions should be visible.

Enrico

.