What question did this study set out to answer?

The aim is to analyze Fermat numbers using the Temporal Dynamics Framework focusing on resonance and decoherence.

April 15, 2026Open Access

Fermat Numbers: Computational Analysis Through Temporal Dynamics Framework

Key Points

The aim is to analyze Fermat numbers using the Temporal Dynamics Framework focusing on resonance and decoherence.
Applied resonance and decoherence analysis to Fermat numbers F_n = 2^(2^n) + 1.
Reviewed the only known Fermat primes: F_0, F_1, F_2, F_3, F_4.
Used diagnostic figures for visual data representation.
Leveraged Wilfrid Keller's Fermat factorisation database.
Identified resonance decay patterns in Fermat numbers.
Analyzed factorization structures related to Fermat primes.
Examined Universal Prime resonance values and their implications.

Abstract

This paper applies the Temporal Dynamics Framework resonance and decoherence analysis to Fermat numbers Fₙ = 2^ (2ⁿ) + 1. The only known Fermat primes are F₀ = 3, F₁ = 5, F₂ = 17, F₃ = 257, and F₄ = 65537. The analysis examines resonance decay patterns, factorisation structure, Universal Prime resonance values, and provides a dashboard analysis. Four diagnostic figures are included. The paper acknowledges Wilfrid Keller's comprehensive Fermat factorisation database. Paper 32 in the Temporal Dynamics Framework Research Series.

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James Norman Ibbotson

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Fermat Numbers: Computational Analysis Through Temporal Dynamics Framework

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