>>6814

Hi, thanks for the question. No I don't want any personal credit for this. I have a family, a career and mild Aspergers. I'm also a recovering alcoholic/addict. Fame, infamy or money would only end in a quick death pursuing women, drugs and alcohol into the gates of death. It wouldnt be my intention, but that is exactly where it would lead after just one drink. That's all it would take. But it is valuable to demonstrate that there is a whole world of maths and engineering that is waiting and using mathematical objects to solve problems in the virtual and real world in this way could open up a new dimension, so to speak.

Other anons can make the billions but I don't have any needs except the thrill of finding no problems to solve and helping the group effort to make the world better where I can.

The only way forward for me is to be helpful and share ideas.

If it sounds altruistic, it's closer to self preservation.

Maybe with a few years of recovery under my belt?

Prolly not.

Now, my computer is frozen (the new one) as soon as it's up and running, I'll write the e column definitions with RSA 100 and 2048, to show how easily everything scales up and to give examples for knowns and unknowns.

>>6817

*new problems

Please also anons, choose caution as the temptation to use this maths for hacking is huge.

Bitcoin has been talked about before.

Bear in mind that this maths can lead to shortcutting the mining process before it can be used even to do anything else.

Second laptop is not functioning.

Before I attribute it to malice, I will let it run to apply background updates.

Hasn't been switched on in a while.

Do not worry.

I have this week off work too.

I will keep you updated.

Computer that can be connected to the internet is now functioning.

Wife is binge watching The Handmaid's Tale right now with it, which rewards her patience this very hot afternoon and allows me to check it's not spiking on CPU or network traffic as this will pause the show.

Once she is done (still recovering from jetlag) I'll install VS C# and it will be a number storm for a couple of post.

We'll be looking at values in a[t] a lot with examples.

As an exercise, can you find BigN-1 in column -f in terms of t? This is unfair as I said I would walkthrough but need to balance a wife who has gone the extra mile and patient anons.

Meanwhile, Q has been very quiet.

Something big happening?

While we wait, just to go over the solution.

The Grid called The End is a superposition of all products where those products are the difference of two squares. This includes all odd numbers and even numbers that are zero mod 4.

Row 1, n=1 is special, since all factors of all products are present in it and by knowing d and e, and calculating f, this superposition collapses into a method to use cells e and -f in the first row, which are unique to d and e.

If there are more than two prime factors, d and e are the same, you can just find the largest two first, one will just be the product of further primes, divide and go again.

The problem we are trying to solve appears to be one where we don't have enough variables known in the equations we have.

The different factors (n-1) in -f, and n in e, coupled with BigN in e AND BigN-1 in -f as well as their 'shadow' partners where they exist at a[c+1-t] give us enough information to determine 1. Is the number prime 2. The value of x.

Remember, x is related to t.

So, for this problem, the 'superposition' collapses on two variables, d and e.

That was my assumption back in 2010 as it happens, that these two properties of c would be enough to factorise.

Integers are not a number line.

They are a family that grows like a fractal tree.

This work can probably be optimised.

There are more ways to do this, as implied, one just uses column zero. The other uses the diagonals but all are related. Like turning a higher dimensional object in 3D. It can look different.

>>6829

>>6831

I would love to buy physical copies of your work Tops.

Elliptic curves are DEFINITELY related.

The universality of the extended Riemann zeta function, the Mandelbrot Set. Related.

Whether you like to get lost in the beauty of colourful representations or found in the ruthless logic of it all, there is something for everyone.

>>6833

Nice.

Thanks for waiting just a bit longer.

Looking at morning UK time to get started as I am still limited to a phone.

A few extra reminders…

t is the order of members in a cell

In the first row where n=1, t gives a values of x that alternates between odd and even.

The value of x in e and -f will never both be even of odd since the gap between the column is always odd or 2d+1

a[t] is half the square of x plus e for the column

When e is larger than x by more than 2x+1, the value at a[t] will be found in a previous column in the first row.

For odd e, x=2t-1; even e, x=2(t-1)

a[t]=(((2t-1)(2t-1)+e)/2, (((2(t-1)2(t-1))+e)/2 for odd, even e

d[t]=a[t]+x[t]

In the rows below the first, where n>1, have you noticed that there is sometimes more than one set of products in the cell?

If there are two, both are growing by 2n added to x in that cell. The first set you can spot the same starting value of x from the value of x in the first cell at n=1. The second begins at -x until adding 2n makes it positive. I'll show this in the other thread after the walkthrough, if anyone is still interested at that point!

Morning anons, have woken in the night with the kind of sore throat I haven't had since I was little. Horrible timing. This should only push things to tomorrow or hopefully this afternoon. Feels like swallowing broken glass.

Thanks for the questions since last night, I will get to them once I can.

Anyone have recommendations besides Manuka honey?

Brilliant ideas.

My wife made a manuka honey drink with a berocca, plus coffee, plus paracetamol, plus this throat numbing thing.

Just doing the install of VS so can use some proper numbers.

I cannot quite believe the amount of the Spyware that comes these days on a cheap laptop. They don't even try and hide it any more.

Customer experience is second to full on data gibs.

Important to get the trip correct.

Brain at 70%

When we start, we'll build some functions.

We want to get a[t] (some na) for a column. We supply the column e and the t. The return is a[t].

Then we want to show that if p is a factor of a[t], p is also a factor of a[p+1-t] for some column e.

>>6857

Good question.

>>6859

Another good question.

Should be ok until the moment the correct factorisation of RSA 2048 appears or just before.

This isn't about hacking or breaking encryption, that's a consequence. This is solving a math problem.

Nothing illegal is occuring here.

Also, nothing attracts attention like having linux pop up from a USB drive all over the place. That's got hacker written all over it, right?

Hackers don't use £200 laptops with Micro$oft on them.

//Function. RoD key pairs

//given two columns, which values of n are separated by 1, where e(n)>-f(n)

//Returns one pair for primes, two for product of different primes, etc.

List<BigInteger[2]ColumnKeys(BigInteger minus_f, BigInteger e);

{

List<BigIntegerresult = new List<BigInteger>();//list to return

BigInteger 2d_plus_1 = e - minus_f;

BigInteger _2d = BigInteger.Subtract(2d_plus_1,BigInteger.One);

BigInteger sqrt_2d = Lib.Sqrt(_2d);