It is true that if n is prime, then  (this is a special case of Fermat's little theorem), however the converse (if  then n is prime) is false, and therefore the hypothesis as a whole is false. The smallest counterexample is n = 341 = 11×31.
The assertion that if n is prime, then holds true, but the reverse implication (if  then n is prime) is incorrect, rendering the overall assumption invalid. A counterexample of the smallest magnitude is n = 341, which equals 11 multiplied by 31.