__What is the Ex0-Prime-Advanced-Tool?__

Thanks to our research, we have developed a way to significantly speed up the processing speed of conventional number primality verification algorithms such as the famous "Miller-Rabin" algorithm and the no less famous derivatives of "Fermat's theorems" that are being used in most current mathematical computation systems (eg GMP / IMP Libraires).

Moreover, thanks to our algorithmic techniques we can not only check the primality of the numbers, but also find all the next occurrences of prime numbers in a consecutive emergent list, as well as all the previous occurrences.

This method allowed us to develop a tool to check the primality of numbers without any size limit, the only limit being the power of the hardware of the machine on which the process is performed.

This tool also makes it possible to generate lists of consecutive and ordered prime numbers, increasing and decreasing, containing the following details:

- Registration of all emerging primes algorithmically resolved live
- Save prime numbers in differents numeric values (Decimal / Binary / Hexadecimal / or any other customizable numeric bases).
- Register actual and exact position of each prime number (if starts from scratch or resuming from an existing database).
- Gap between each prime numbers contained in the generated list.
- Identification of the nature of each prime number solved sequentially (TWIN / TRIPLE / QUAD / SEXY / CONSTELLATION)
- Inscription of the TICKS time index for each emergence of resolved prime number.

The **Ex0-Prime-Advanced-Tool** allows to generate parametrable lists of prime numbers according to the needs:

- Manually set the starting numeric value of the list or retrieve it from a previously calculated database in order to complete it.
- Generation of lists in Incremental mode (eg 2..3..5..7..11 ...) or in Decremental mode including the negative mirror values (eg 3..2..- 2..- 3..- 5..-7 ...).
- Length of the list is equivalent to the quantity of prime numbers desired or defined by the maximum numeric stop value of this list (possibility to automatically split the lists with a threshold defined by the number of lines that can being stored inside each numbered list)
- Display of the list generated in a console for quick tests (do not choose this option for large lists, this greatly reduces performance).
- Export to txt / xml files or in synchronization mode with a database (creation of a new database or resume of an existing one).

The allocable hardware resources are also configurable and the user can choose how they should be used by the **Ex0-Prime-Advanced-Tool**:

- Enable and set the export compression as well as the output format of the generated lists (a large compression allows an excellent reduction of the final size of the exported data but significantly slow down the speed of execution of the calculation process).
- Available free disk space security margin when exporting lists to txt / xml files or to a database (Specify the minimum space size that should remain free on the storage unit before pausing of the tool: minimum 5 GB must remain available on the unit)
- Physical quantity of allocatable RAM (Auto: 90% max / Manually: 97% max)
- CPU-allocable resources (Auto: 90% max All-Cores / Manually: choose each CPU-Core independently and set their usage up to 99% independently)
- CPU-Mono-Thread or CPU-Multi-Thread calculation mode (the Multi-Thread mode greatly improves the speed of processor calculation, but only the Mono-Thread mode allows the emergence of a temporal sequence with an exact chronological TICKS sequence ).

It is also possible to run comparative tests between the different available algorithms:

- Activate or deactivate the
**Ex0-Prime-Checker**function (Algorithm developed by Ex0-SyS to optimize the processing of conventional algorithms for verifying the primality of numbers) - Selection of conventional algorithmic calculation mode (Miller-Rabbin / Frematt)
- Conventional algorithmic computation accuracy level (default is 10)
- Customizable numeric values used to allow a better accuracy of the set (default 3 and 7, each value separated by a comma without any other constraint)

The **Ex0-Prime-Advanced-Tool** tool allows Multi-Instance execution of the application offering the possibility to perform several separate tasks in parallel with each their own parameters and this in a balanced way concerning the percentage of assignment of the material resources between each instance.

This application is also intended to be configured as a service allowing deployment on large infrastructures in clusturing mode and / or network with assignment of fragmented calculation batch on several physical units.

The **Ex0-Prime-Advanced-Tool** is currently the most powerful tool for checking and generating consecutive sequential lists of prime numbers accessible to all.

For more information on this project, do not hesitate to contact us.