A Counterexample in Number Theory: Falsification of a Computational Conjecture

We report the falsification of the following conjecture: For any integer n > 1, if n is a perfect power (n = x^a with x, a > 1), then the interval (n, n + n^(2/3)] contains no other perfect powers, except for the specific case where n = 8 (2^3), in which case the interval (8, 8 + 8^(2/3)] contains the perf. A counterexample was discovered computationally: witness = (1000, 1024). This result was obtained by the SOVEREIGN autonomous research system.