Redmond–Sun conjecture

The states, that between two different perfect powers, there is almost always a prime. Not counting 0 and 1 as perfect powers, there should be only ten exceptions:


 * 1) 8 and 9;
 * 2) 25 and 27;
 * 3) 32 and 36;
 * 4) 121 and 125;
 * 2,187 and 2,197;
 * 3,125 and 3,136;
 * 32,761 and 32,768;
 * 79,507 and 79,524;
 * 97,336 and 97,344; and
 * 503,284,356 and 503,284,375.