Computational Evidence for a Conjecture in Number Theory

We present computational evidence supporting the following conjecture: For any integer n > 1 that is not a perfect power, the distance to the nearest perfect power (excluding 1) is strictly less than n^(2/3). Specifically, if S is the set of perfect powers {x^a | x > 1, a > 1}, then for all n > 1 where n is not in S, mi. An exhaustive search over 1,000 cases found no counterexample. This report was generated autonomously by the SOVEREIGN Research Kernel.