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Sophie Germain Primes: Computational Analysis Through Temporal Dynamics Framework | Synapse

April 15, 2026Open Access

Sophie Germain Primes: Computational Analysis Through Temporal Dynamics Framework

Key Points

This research aims to analyze the properties and implications of Sophie Germain primes using resonance analysis.
Applied the Temporal Dynamics Framework to study Sophie Germain primes.
Conducted resonance analysis on the structure of safe primes.
Investigated the relationship between Sophie Germain primes and Fermat's Last Theorem.
Identified specific patterns in the modular resonance of Sophie Germain primes.
Clarified the structure of safe primes related to the findings.
Demonstrated potential applications in cryptography with the identified primes.

Abstract

This paper applies the Temporal Dynamics Framework resonance analysis to Sophie Germain primes, where p is a Sophie Germain prime if both p and 2p + 1 are prime. The safe prime 2p + 1 structure is analysed through Universal Prime modular resonance. Sophie Germain primes have applications in cryptography and are related to the first case of Fermat's Last Theorem. Paper 22 in the Temporal Dynamics Framework Research Series.

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Authors

J

James Norman Ibbotson

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Cite this study

James Norman Ibbotson (Mon,) studied this question.

www.synapsesocial.com/papers/69df2c50e4eeef8a2a6b1499 — DOI: https://doi.org/10.5281/zenodo.19544219