Use your wit
That's a good idea. I was looking at some polynomials they use for the GNFS and it dawned on me just how useful it is to represent c as a sum of powers. So when you factor d and e, it's meant to decompose the dd+e equation into (factors of dd) + (factors of e).
And decomposing dd+e further into squares is definitely leading towards calculating the i^2 - j^2 equation.
I believe we're making a lot of progress.
No lead on that so far. Just seems like sum of squares as c has to be related to difference of squares as c.
I see a pattern in them and I'm not crazy. Something that scales with c in a way that's hidden from the algebra.
Chris said the remainder tree resembles the solution. Decomposing values into powers of 2 and triangles resemble the remainder tree. And if all 3 of those can solve, it must be something they all share that makes them able to do that. Plus, you can probably use a simple equation to transform each term of each sequence into the other. The grid has those sequences.
Maybe it's just something obvious, like if you make everything tiny then that makes the search space tiny too.
That's what I tried to do with the infinite triangle sequences. If you remember, the end result was a number that would get pretty close to (X-x)/2 of c for some reason.
It was easy to make the search space small enough to count on one hand, but you had to be able to traverse back up the remainders.
Maybe there's something that can tell us what the next remainder is
Perhaps if we can create like a phantom c that is easy to factor but also has a self-similarity to the large one? Seems like a way to check an answer
Ideas are insightful until proven otherwise
I never identified one
The grid has always enhanced or shown how uninsightful something was when I added it to it.
I think an overarching theme here is you can use a variety of estimates if you're actively making them relate themselves to c.
Kind of like the original tree being a "big picture" estimate program and the tree cells being a more "zoomed in" version since they use more information from the grid.
π(c) = amount of primes <= c
π(145) = 34
π(2537) = 370
π(6107) = 796
With the Riemann Zeta function ofc
Made a thread for PDFs
Seems to me there is a reason n0 and the f mod stuff were given as "from arbitrary guesses" ie, differing guesses can still be adjusted to reach the factorization.
Don't mind this, just some junk
I have a feeling we wil be working on ECC very soon
Here's a sample ECC key on curve nistp192. I threw away the private key.
(3869035562762729475071350689725296476315431951714456492369, 5721900778986487358975428077347210421279593804122562127173)
Efficient factoring instantly breaks discrete logs, though. So it'll be two ivory towers falling at once.
Discrete logs are just factoring but with the same factor to some power.
Remember, Shor works for both in polynomial time.
It really was the biggest hint since the start, thank you!
Didn't realize I'd have to bake this soon. Gives me a chance to fix the codebase. I am feeling the acceleration.
Let's go through all the threads!
All the threads, all the math!
I have said these things to you in figures of speech. The hour when I will no longer speak to you in figures of speech but will tell you plainly about the Father is now.
I and the Father are one. No one who denies the Son has the Father. Whoever confesses the Son has the Father also. Whoever confesses that Jesus is the Son of God, God abides in him, and he in God.
What's a chan we can set up on if shit hits the fan for 8?