>>6627

True for all c where c is the difference of two squares. That includes the product of any two odd numbers. That includes the product of any two prime numbers.

That puts the row of the product of two prime numbers at rows n and n-1.

That difference is the key.

It means that columns -f and e have a property that can break the equation deadlock.

That property and those columns are unique to each c. They are dependent on d, e and therefore f.

As stated at the start, the square root of (D)avid and what remains are the key to unsealing the The End, the grid.

It will all make sense.

Especially the triangular part.

This is the beginning and The End.

I'm just a messenger.

This has always been about (you).

>>6624

Almost.

That n-1 is a factor of col -f and n is a factor of e will show you a shortcut to the triangle solution.

When it all comes together, you'll see shortcuts everywhere.

And this is just mathematical object that this can be applied to.

>>6619

Love your printouts and your approach. Very similar to what I did.

>>6618

How will it End?

Do not be afraid of negative x values in row 1 for -f and e.

You've been patient enough.

The next step will take a few days.

Tomorrow we will start the walk through of the largest RSA number.

The reason it will take a few days is because it will be methodical and each part of the step will have a relevant example calculation.

RSA 2048 is a large number but simple to use with the BigInteger library.

We will walk through each relevant part of the grid and show that the pattern holds for RSA 2048 with the calculation that you can perform yourself.

To my knowledge RSA 2048 has not been publicly factored by anyone else.

At the end of the parts of the step, it will be the proofs you deserve.

I really appreciate your patience, it will be worth it because you will follow everything in the breakdown of the grid patterns.

Everything will tie together.

>>6718

Nice.

>>6729

Because the RoD approach has Big Oh the same as the square root function, it doesn't matter how big they are, they would be insecure and too impractical to use.

First, we will go over some properties definitions and build functions.

This is interactive, so you will be doing the checks at each part.

The Grid is also called The End.

The Grid has cells.

Each cells has zero or infinite elements.

That a cell has infinite elements if it has any, is the first part to show.

An element represents a product, c.

c is the difference of two squares.

ab = c = dd + e = (d+n)(d+n) - (x+n)(x+n)

An element that represents a product c, the difference of two squares has a column coordinate and row coordinate.

The column coordinate is e, the remainder of taking the largest square with sides d.

The row coordinate is n, the amount added to d to make the side of the larger square in the difference of two squares. n is also the amount added to d to make it the mid point of a and b.

Each cell has coordinates (e,n)

Each cell element has coordinates (e,n,t) where t is where the element comes in the cell if ordered by size of c.

Each element c in a cell has the properties (e,n,d,x,a,b)

e is the remainder and column

n is the amount added to d to make the large square

d is the square root of c

x is the difference of a and d

a if the smaller factor of c if not equal to b

b is the larger factor of c if not equal to a

If a cell contains an element c, another element in the cell can be constructed from it.

Call it c'

e' = e

n' = n

x' = x + 2n

a' = b

d' = a' + x'

b' = a' + 2x' + 2n

Once c' is constructed, c' becomes c and the process is repeated ad infinitum. e and n don't change, which make sense since these are the coordinates of the cell.

Any questions on that?

It holds for all cells.

We can do a proof by induction, if anyone would like that?

I'm phone fagging as my computer won't start so I'm picking my spare up later when I watch the football.

Don't need many resources to walk through, just something with BigInteger library when we get to the RSA numbers.

We'll do all of them when we finish the biggest, as we'll build the algorithm as we go.

Let me know if we want the proof by induction for cells being zero or infinite in count of elements or if the construction above is enough. Also, if anyone wants to take a stab at the proof by induction, that would be a good practice.

>>6737

'Morning' Top.

Beautiful day here.

Prediction against Sweden?

For when this thread hits post limit, I've created #13.

When at least one regular or two anons confirms they are happy with the constructibility of cells to be zero or infinite in elements, we'll move on.

>>6744

>>6744

Great, feel free to delete the new one.

Thanks for the confirmation.

Next, we show how to calculate BigN of an odd number.

All odd numbers are the difference of two squares.

The product of two primes, is the difference two sets of squares.

Every odd number is the difference of two consecutive squares.

The value of n for the product of 1 and c is defined now as BigN for odd numbers.

Since d-a=x and x+n is the smaller square in the difference of two squares, then for odd numbers, BigN is ((c-1)/2)-x

x is d-1, since a=1

Anyone want to show:

RSA 2048

c=RSA 2048

d=

e=

BigN=

Remember BigN is the row in column e, where we always find (e,n,d,x,1,c)