25 years ago the Western empire snubbed me. They were powerful they looked hard and almost unstoppable, they were prosperous and strong.
I Marched like a soldier in the other direction against all the surf and tides.
Then I was seen as mad and trying to think the impossible could happen.
Today no one is laughing.
However the new empire is not the old one but they have snubbed me.
March I shall.
I can't go West I can't go East.
But then again China is not India.
China is not Africa.
China is not South America.
And I am perceived as a white westerner an outsider yet again.
I must be mad to think I can march in that direction.
But march I shall.

Just like 20 years ago China and their new empire are strong, prosperous and powerful and this new journey of mine will be hard and also China is not the old Western one so this course will be different and near impossible yet again. Just like 20 years ago it is in my view unnecessary but attack me they do.
So march I will.

So far I can find a wide ranging upper and lower bound for my lowest co prime in a 2 co prime composite then I can find a small bunch of smaller bounding's within. The Question I have is can I then end up with a fractal like program wher first it analyses the 2 co prime composite then it does the same analysis in the smaller bounds until I can go no future with my number and my prime will be in one of a far larger range of tiny bounding spots upon which I then use a Gambling function which will in the end find my co prime but that with the right timing and parallelization gives me better odds then a sieve'ing mechanism on top of the efficiency benefits of only having to look in small crevasses.

This should save me much time and memory considering what I already have achieved when searching for a semi prime/co prime.

Another tool which might up my odds if tuned right could be the what I call MMod or multimod.
So MMod or MultiMod takes and orders from largest to smallest a range of mods which it adds up and as the main Moding and divides into subsections equal to and between the ranges. This technique offers the ability the ability of of having a two tier Mod function.
This from Idea from even very early testing is already displaying interesting results which could be very useful for gambling fast and with good odds of finding the desired number quickly when use in a Gambling test.

When dealing with the issue of factorising a 2 co-prime composites.

So far I can find an upper and and lower bound for where I will find my lower co prime.
With that information I can then find a few (about 80 or so for RSA230) slots between where each of the few slots have a far smaller lower and upper bound and my co -prime will be somewhere between the upper and lower bounds of one of the slots.

This Math I am developing would greatly improve the amount of checking a general number filed sieve method requires.

I donno What the NSA/Chinese Intelligence has right now considering P almost definitely equals NP but for cracking 2 co-Prime Composites greater than 100 bits and smaller than 512 bits on the cloud and for some low bit numbers at home this work could become quite useful even for far faster factorisation below 100bits.

the 2 maths techniques I am using run at approx O 2(log N) and the other at approx O log(2,N)/log(3,N)
So they are fast but for very large numbers you would still be left with quite a range to check for your CO- Primes roughly N / Log(N) / (Log(N)^3) slots which is still a lot of number space to check for big Integers.

Alongside this I have already developed an approx O(13) run time between weak and strong Probable prime test which may or may not be of some use here.

I achieved this math with Wieta Temarkon and will be posting more on GitHub anonymously probably sometime next year.

I am but one maybe clever maybe mad person the NSA ect has most of the best mathematicians in such fields as cryptography. If you look on the Wikipedia at the RSA numbers section it Implies that a quantum computer could be built to tackle such things as maybe even Integers 4096 bits in size and if Edward Snowden has demonstrated with information they are watching everyone and everything they can and almost certainly are ahead of me when it comes to cryptography and aware already of all my work.

If you then look around the internet at people claiming RSA is fully hack-able they are laughed off on the given forums yet if you now look at the p vs np pages on the wikipedia or else where it is very hard to ascertain what exactly the fastest solution to an NP complete currently is as what ever it is it will be the fattest that any NP problem can be solved because NP complete problems can be used with very quick conversion to solve any NP problem.

To understand what an NP problem is lets look at chess. Now chess is not actually NP as far as anyone knows but chess is a good way to explain the issue. It's very easy to check if you have won your game of chess but very hard as far as we know to know the best move to make in any situation on the chess board. chess as far as is known is actually a exp complete problem and not NP but thats still up for debate and research as it is not known if chess is or isn't NP. an NP problem would be something like Sudoku now Sudoku is easy to check if you have won much like it is easy to check if a given Prime number divides into a given composite but harder to find a number that does fit.

Lets go a little more into depth.

so P time mean this say I had a P time algorithm that solved sudoku. my algorithm would look like this.
lets say we are dealing with a 81 square grid so x will be 81

Solver(x)
"Start"
If you have done function 1 x amount of times then stop and give result other wise do function 1

Funtion1(x)
do this x amount of times
then go back to start


So over all you will have done this x^2 times as you have x amount of calls to function 1 and function one does this x amount of times.

such a program would be O x^2 in sudoku's case this would be a maximum of 81^2 operations

Until recently at least no such program has existed for any of the NP complete problems like Sudoku
The only solutions were just below a maximum of O 2^x operations although for many 81 square sudokus a solution could be found far faster the maximum time it took was still in exponential time...

[ Continued ]

The Basic tools of Wieta Temarkon.

First you have Temarkon.

Which comprises of 4 basic sets of Bases
23 Hindu (Power Series)
32 Hindu (Power Series)
&
23 BiJective (Geometric Series)
32 BiJective (Geometric Series)

These 2 sets are closely related and...
I believe are relevant to the natural patterns of numbers. If
you had floating point logarithms derived from these bases then you could I'm pretty certain go straight down the middle of the Prime Number distribution without much more effort you certainly would at the very least get a very close estimate of Prime Nth although so far I have only deduced Floor(Log[23or32,N]) not the full log.

Then you have Zequeba.
Zequeba represents a function for dealing with all the issues relating to the digits of Temarkon representation. It's kinda my Digit Play function.

Then you have Totarngular.

Totarngular is where you count relative to Algebraic geometries in a given dimension.
I achieve this by counting with as many numbers as there are dimensions I am counting in.
so in 2D relative to the Triangle Numbers so far I can do upto 6D but heres 2D.
inp 1 out {1,1}, inp 2 out {1,2}, inp 3 out {2,1}, inp 4 out {1,3}....
And with Totarngular Triangle Number dim 2 you can do the reverse and input your 2 output numbers and output your your original number thus at least as far as integers are concerned your 2 numbers have congruence and together they have equality and parity with your original input number.

TheQ.
A very simple Q is this.
so -1=-2 and 0 =0 and 1=2.
In this Q no Input number can go between -2 and 2.

Dynaveo
Dynaveo is like a parallizible self playing piano that can alter the note sheet.
first you have a test from tests list then is the conditions of the test are meet you skip say 2 slots on either of the operations lists which can go round like a clock. Depending on what has happened you event can either tell another dynaveo to change alter operation list or the rule list or it can output to the output list ready for when the dynaveo is called to give current output.
Dynaveo is more powerful than neural netting as is more open It can mimic a neuron better than a standardised neural net(with no way near as much efficiency more ideal for modelling individual neural activity) but it can also do a lot more computer like stuff.

Relationship and Tie.
Relationship and tie is a VIVD function like Dynaveo but it's more for modelling systems at the base either for assembly coded engines or for IC development.
R&T is Ultra CISC'y and highly parrallelizable.
You have a set of piecewise bitwise functions that are Tied and that can relate.
The input can be varied of 2 binary digits per digit representation and separated and opp coded
From this the idea is to model a system which does Wieta well via 6 to 12 steps of R&T.

I hope one day to unify Wieta Temarkon as to have a powerful enabling tool set running well on my computer I certainly always am working on the functionality of what I have.

The Kernel system.

A disk manager which only manages 2 types of files drset(driver sets) files and bdset(Binary data sets). the sets are like binary level dbase files that can contain standard files nad compiled/decompilable Html5&Wasm code in them.

A swap drive/partition management.

Media drive/partition caching.

A subsystem giving good systems access to drset files.

Base file encryption system allowing for individual drset fileset encryption and biometrics + SHA 2 sizing up for some of the upper engine.

Power management sub system.

The Main System.

Optimorph GUI engine allowing for morphic windows which can shift between multiple apps and keep a task icon load memory of each app its running different from a standard task bar or multiple desktops in that all apps running on one app explore are accessible for turning off ect in that particular app exploration. The reason for this is that you can have more control of an app instance for example if you are doing some work which required a few apps and you want to drop the work into the cloud bag for people you have chosen to edit or add foot notes to you can. Or if you want to run all the apps in that instance through a proxy or Tor you can. Or if you want to white list the access of all those app instances in the app exploration instance you can. In fact with this system you can even record your own instance setup or moment and link this starting point or resume point temporary to your main access menu.

A given app instance can be set to only accept tablet or mobile phone format and you can have an app just for view tablet or mobile phone versions
of a web site as a web sites and an apps on this system are synonymous.

The driver sets all written in Assembly.

Disk and separate drset file encryption system where by you can encrypt vital driver sets with different keys for biometrics to better control access.

Ultra precise Sandboxing of apps and app instances controlling what access each app gets to drivers and other apps.

An OPEN GL/OPEN CL drivers set allowing custom modding for various different GPU types and co processor types.

A Soft effects library/engine which can be hardware enhanced.

Power management upper engine system (for fine tuning system perfromance and demands).

A File conversion library drver for converting files.

An Anti dos attack Chaotic network loading system to advert signal processing of dos attacks.

A Firewall system that hides you well and allows for port and address management and Grasdualy optimized AI whitelisting.

Device access control for IOT sercurity.

Gradual rate Optimisation AI performance management Also so that your system as you use continues to adapt well to demand.

A web code engine for fast WASM and HTML5 offline/online web apps to be contained in bdset files with drv's allowing for HTML5/WASM machine specific extensions for registered with system apps.

Bit trail indexing system for fast optimal access to system data where trails are left for search optimisation relative to use and community input with all fast bitwise seeded for ultra fast searching of data on the general system data down to data elements.

Back Wards Compatibility say when HTML 6 is more official to be emulated or if a new kernel is written the older stuff is to be emulated.

Notes...

The Idea of this system is for high security, usability, re-engineer-ability, optimisability and better group working over the internet.