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MicroPrime

Experimental project for prime number exploration based on the GC-60 model

Overview

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.


Core idea

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.


Experimental validation (summary)

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.

GC-60 model overview

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.

See:
docs/GC_60_overview.tex


Project structure

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.


Incremental archive

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.


What MicroPrime does

  • 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

What MicroPrime does not do

  • 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.


Intended audience

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.


Project status

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)

Citation

If you use MicroPrime or refer to this project, please cite the Zenodo record:

https://doi.org/10.5281/zenodo.18141354

License

This project is released under the MIT License.
See the LICENSE file for details.

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Experimental project for prime number exploration based on the GC-60 model

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