How do I disproove this by counterexample? If $2^n-1$ is composite then $n$ is composite.
Where n is larger than 1
How can I disprove this using a counter example? 

It is well known that $2^n-1$ can only be prime if $n$ is prime (A prime of the form $2^n-1$ is called a Mersenne-prime)
But the converse is not true. There are primes $n$, such that $2^n-1$ is composite, for example $n=23$, refuting the claim. The first few counterexamples are
? forprime(p=1,100,if(isprime(2^p-1)==0,print1(p," ")))
11 23 29 37 41 43 47 53 59 67 71 73 79 83 97
?

