Fermat Numbers: Computational Analysis Through Temporal Dynamics Framework

This paper applies the Temporal Dynamics Framework resonance and decoherence analysis to Fermat numbers F_n = 2^(2^n) + 1. The only known Fermat primes are F_0 = 3, F_1 = 5, F_2 = 17, F_3 = 257, and F_4 = 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.