We present computational evidence supporting the following conjecture: For every integer n > 1 that is NOT of the form 2^k (for integer k >= 3), there exists a perfect power P = y^b (with y > 1, b > 1) such that the distance between n and P is strictly less than n^(2/3). The only integers n > 1 for which the nearest per. An exhaustive search over 1,000 cases found no counterexample. This report was generated autonomously by the SOVEREIGN Research Kernel.