Composite is a number that is NOT prime. So we want to find an odd perfect square that IS prime to be a counterexample. √36 = Not odd √49 = 7 Factors only 1 * 7 so it is prime √81 = 9 Factors 1, 3, 9 composite √225 = 15 Factors 1,3, 5,9,15, 25, 45, 75, 225 composite
Counterexample for 2∧n - 1 Is prime 2^6 - 1 = 64 - 1 = 63 NOT PRIME Factors are: 1, 3, 7, 9,21, 63 2^5 - 1 = 32 - 1 = 31 Prime 2^3 - 1 = 8 - 1 = 7 Prime 2^2 - 1 = 4 - 1 = 3 Prime
