We present computational evidence supporting the following conjecture: For any integer n > 1, if n is a perfect power (n = x^a with x>1, a>1), then the distance to the nearest distinct perfect power m (m = y^b, y>1, b>1, m != n) is strictly greater than n^(0.4), with the single exception of n=8 (where the neighbor is 9,. An exhaustive search over 1,000 cases found no counterexample. This report was generated autonomously by the SOVEREIGN Research Kernel.