The Resonant Order Theory of Everything (ROTE) proposes a universal framework where physical systems, from quantum to cosmic scales, emerge from a ψ\psiψ-spaced spiral shell structure governed by the equation r(n)=r0⋅ekn r(n) = r_0 \cdot e^{k n} r(n)=r0⋅ekn, with n n n as the spiral index and k≈0.233 k \approx 0.233 k≈0.233 for planetary orbits. Its Prime-Null Accord posits that prime n n n-values act as forbidden zones, preventing stable orbits due to destructive interference. This study tests the null hypothesis that gaps between consecutive planetary orbital radii (Mercury to Pluto, including Ceres and Kirkwood gaps) avoid prime n n n-values. Using k=0.233 k = 0.233 k=0.233, derived from the Saturn-Uranus gap, spiral indices were calculated, revealing most gaps (e.g., 2.68, 1.39, 1.81) avoid primes within a ±0.1\pm 0.1±0.1 tolerance, with only two near-prime gaps (2.98, 1.92). Statistical analysis (p-value 0.575) supports the null hypothesis, aligning ROTE’s predictions with observed exponential spacing akin to the Titius-Bode Law, suggesting robustness in explaining solar system structure.