MicroPrime v3.0 – Gap-Based Archive Optimization

MicroPrime – Optimization of Informational Revelation

The MicroPrime project evolves the management of its divisor archive by moving from a structure based on offset modulo 60 to a storage model based on Gap (Delta Encoding).

This update does not represent a simple reduction of disk usage, but a structural simplification of the logic used to reveal prime numbers, that is, the process by which divisors are extracted from the archive and projected into the search window, extended up to the square of the archive value itself.

The system now assumes a hybrid nature:

• prime number searching continues to follow the logic of the GC-60 method
• data storage is performed using Gap (Delta Encoding)

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Logic of the Change: From Complexity to Linearity

The divisor archive is the informational engine of the GC-60 model.
In order to use these divisors within the study window, each prime number must first be revealed, meaning reconstructed from the stored data.

Previous Method (Offset modulo 60)

Revealing each single prime number required a chain of mathematical operations:

• multiplications
• modulo calculations
• additions

Repeating these operations over millions of records generated a significant computational load during the projection of divisors onto the global search window.

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New Architecture (Gap – Delta Encoding)

With the transition to Gap-based storage, the mathematical structure is radically simplified.

To reveal the next prime number, the system now performs:

• a single addition

The sequence of prime numbers is reconstructed linearly through the progressive summation of gaps, completely eliminating multiplications and modular operations.

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Practical Advantages

This change produces two immediate benefits:

1. Reduced memory usage
   For the same number of generated archives, Gap-based storage occupies about 30% less space than Offset-based storage.

2. Faster loading and reconstruction of prime numbers
   Divisor revelation is performed through simple additions, reducing the computational cost to the minimum hardware level.

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Experimental Verification

The experiments carried out have shown that the two systems produce mathematically identical results.

The comparison between Offset and Gap archives gave positive results on initial, intermediate, and final files:

File_offset 0000 ↔ File_gap 0000 → identical
File_offset 0350 ↔ File_gap 0350 → identical
File_offset 0636 ↔ File_gap 0636 → identical

This change does not modify the structure of the global archive in any way:
individual archives remain independent units thanks to the metadata stored in each file.

The archive implementation remains unchanged and can be resumed at any time whenever further expansion is desired.

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Additional Features in This Release

In this release, a JSON File Editor has been added.
This editor allows users to load the files saved during searches for further analysis and to export them as PDF documents for cataloging and documentation purposes.

In addition, the file librerie.txt has been included.
This file is useful for reinstalling all the libraries used in the program’s virtual environment (venv).

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Notes

The storage folder for the Gap archive is not set dynamically and is currently fixed to:

f:\file_gap

If a custom folder is desired, it must be manually modified in the following two programs:

• gap_McreaV3.py
• gap_MstudiaV3.py

MicroPrime v2.0

This release introduces a new screening mode for the search window
in the Studio module, designed for large or very large search ranges.

The mode is selectable through an explicit option and modifies the
behavior of the screening process compared to previous versions.

An experimental demonstration of the behavior is available in the video:
https://youtu.be/of8muSxsWH8

Post-release note (MicroPrime Create):
A small typo was found in the archive deletion routine at line 61 ("ista_.pkl" → "lista_.pkl"). This does not affect the mathematical logic of the algorithm but may affect the correct handling of the global archive when creating a new archive over an existing one.

MicroPrime v1.1 — Studio interface enhancements

Version 1.1 introduces usability and visualization improvements in the
MicroPrime_studio component.

The core MicroPrime archive engine and the GC-60 arithmetic model remain
unchanged with respect to v1.0.
This release focuses on making execution speed and workflow progression
more explicit to the user during archive and window exploration.

Changes in this release:

• Visual feedback for archive processing and window exploration
• Improved perception of execution speed during searches
• No changes to the underlying mathematical model or core algorithms

MicroPrime v1.0 — Baseline experimental implementation (GC-60)

This release represents the baseline experimental version of the MicroPrime project.

Version 1.0 includes the original implementation of the GC-60 arithmetic model and
the incremental archive system used for prime number exploration.
The code in this release corresponds to the version used for the experimental
validation and statistical tests documented in the associated Zenodo publication.

Key characteristics:

• Incremental and persistent archive based on the GC-60 model
• Separation between archive construction and window exploration
• Prime extraction inside arbitrary numeric windows
• Stable behavior verified up to large numeric scales

This version is intended as a stable reference point.
Subsequent releases will introduce usability and visualization improvements
without altering the underlying mathematical model.