Experimental project for prime number exploration based on the GC-60 model
MicroPrime is an experimental project dedicated to the exploration of prime numbers through an arithmetic model called GC-60.
The goal of the project is not the exhaustive enumeration of primes, but the ability to extract prime numbers efficiently inside arbitrary numeric windows, provided that a suitable archive has been previously constructed.
MicroPrime is designed as an incremental and persistent system: once the archive is built, it can be extended over time without recomputing previously generated data.
The GC-60 model is based on a structural reduction of the natural numbers using admissible residue classes modulo 60.
This reduction removes trivial composites in advance and allows the construction of a compact and structured archive of divisors.
A key design principle of MicroPrime is the separation between archive construction and archive interrogation:
- the archive encodes arithmetic information derived from the GC-60 model;
- prime numbers are extracted only when a specific numeric window is queried.
This approach differs from classical sieves and brute-force methods, which typically operate on a single contiguous range.
MicroPrime has been experimentally validated on multiple numeric scales, up to the order of magnitude of 10²⁰.
Across all tested windows, the measured prime density closely matches the theoretical logarithmic density, with deviations consistently below ±0.02%.
This confirms that the segmented screening process based on the GC-60 model neither omits nor duplicates prime numbers.
The distribution of primes among the 16 admissible residue classes modulo 60 remains uniform (≈6.25% per class), indicating structural stability of the GC-60 model.
The system also demonstrates reliable scalability on consumer hardware, with automatic archive extension and safe handling of insufficient archive coverage.
A complete technical validation report, including performance metrics and statistical results, is available in the associated Zenodo publication.
A conceptual overview of the GC-60 arithmetic model is available in the documentation folder.
The document describes the structural principles of GC-60 independently of any specific implementation, including:
- the use of admissible residue classes modulo 60;
- the concept of an incremental arithmetic archive;
- the idea of localized windows of exploration.
The repository is organized into three main components:
-
MicroPrimeV1/
Responsible for building and incrementally extending the GC-60 archive.
The archive can be created from scratch or extended from the last valid state. -
MicroPrime_studio/
Provides tools to explore the archive, extract prime numbers inside user-defined windows, and compute basic statistical analyses. -
docs/
Contains conceptual documentation describing the GC-60 model and the overall architecture of the project.
One of the defining features of MicroPrime is its incremental archive.
The archive:
- grows monotonically over time;
- can be extended without invalidating previous data;
- allows the computation to be paused and resumed at any moment.
Each archive file represents a consistent and self-contained state.
When additional capacity is required, MicroPrime continues from the last archive file instead of restarting the computation from the beginning.
This design makes long-term exploration feasible even on modest hardware.
- Builds an arithmetic archive based on the GC-60 model
- Allows fast extraction of prime numbers in arbitrary numeric windows
- Supports basic statistical analyses as a secondary, exploratory feature
- It is not a general-purpose factorization algorithm
- It does not claim optimal asymptotic complexity
- It does not provide definitive statistical conclusions about prime distribution
MicroPrime should be considered a research and exploration tool, not a closed or optimized final solution.
MicroPrime is aimed at two types of users:
- Enthusiasts, who can use the software as-is to explore prime numbers;
- Researchers and advanced users, who are interested in understanding the GC-60 model and developing their own analyses on top of it.
The project encourages experimentation and independent interpretation of the data.
MicroPrime is an active experimental project.
- The code is functional and tested
- The archive system supports incremental growth
- A more formal and mathematical description of the GC-60 model is planned for a future publication (e.g. Zenodo)
If you use MicroPrime or refer to this project, please cite the Zenodo record:
https://doi.org/10.5281/zenodo.18141354
This project is released under the MIT License.
See the LICENSE file for details.