The Redmond–Sun conjecture states that, between two different perfect powers (not counting 0 and 1 as perfect powers), there is always a prime, except for the ten cases listed below:

  1. 8 and 9;
  2. 25 and 27;
  3. 32 and 36;
  4. 121 and 125;
  5. 2,187 and 2,197;
  6. 3,125 and 3,136;
  7. 32,761 and 32,768;
  8. 79,507 and 79,524;
  9. 97,336 and 97,344; and
  10. 503,284,356 and 503,284,375.
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