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A prime number is one that only has factors of 1 and its self (3 is a prime number because you can only multiply 1 and 3 to get it). Since you can multiply 1 and 68, 2 and 34 or 4 and 17 to get 68 it is not a prime number.
A prime number has only 2 factors which are 1 and itself. Composite numbers are everything else except 1 and 0. 1 and 0 are neither prime, nor composite. 68 is composite.
68 = 22 x 17
This can be an extension to the proof that there are infinitely many prime numbers. If there are infinitely many prime numbers, then there are also infinitely many PRODUCTS of prime numbers. Those numbers that are the product of 2 or more prime numbers are not prime numbers.