What question did this study set out to answer?

The research aims to analyze the prime generation process using Atkin's sieve through the Temporal Dynamics Framework.

April 15, 2026Open Access

Atkin's Prime Generation Conjecture: Computational Analysis Through Temporal Dynamics Framework

Key Points

The research aims to analyze the prime generation process using Atkin's sieve through the Temporal Dynamics Framework.
Applied Temporal Dynamics Framework to Atkin's sieve
Examined distribution of quadratic forms
Analyzed modular class structure
Validated findings against 78,498 primes
Confirmed existing primes match generated primes based on analysis
Identified distribution patterns in form results
Provided visual diagnostics through three diagnostic figures

Abstract

This paper applies the Temporal Dynamics Framework to Atkin's sieve and prime generation through quadratic forms. The Sieve of Atkin (2003) generates primes using three quadratic forms based on residues modulo 60. The analysis examines form distribution, modular class structure, and validates against 78,498 primes. Three diagnostic figures are included. Paper 38 in the Temporal Dynamics Framework Research Series.

Connected Papers

Building similarity graph...

Analyzing shared references across papers

Discussion

Cite this study

James Norman Ibbotson (Mon,) studied this question.

www.synapsesocial.com/papers/69df2cb9e4eeef8a2a6b1ee2 — DOI: https://doi.org/10.5281/zenodo.19544268

Atkin's Prime Generation Conjecture: Computational Analysis Through Temporal Dynamics Framework

Key Points

Abstract

Citation Network

Connected Papers

Discussion

Cite this study

Authors

Actions

References and Citations

Citation Network

Connected Papers

Discussion

Also consider