Difference of two distinct prime numbers is ?

Concept: whether the difference of two numbers is odd or even, and whether that difference is prime or composite, depends on the specific values chosen -- it is not a fixed property of any pair of primes in general. Since 2 is the only even prime, every other prime is odd, and this parity split is exactly what controls the outcome.

• If 2 is one of the two primes: the difference equals (an odd prime) minus 2, which is always odd, but not always prime -- e.g. 13 - 2 = 11 (prime) versus 17 - 2 = 15 = 3 x 5 (composite) versus 3 - 2 = 1 (neither prime nor composite).

• If neither prime is 2 (both primes are odd): the difference equals odd minus odd, which is even, but not always composite -- e.g. 5 - 3 = 2, which is itself prime, not composite.

Cross-check: so no fixed pattern such as always odd-and-prime or always even-and-composite can describe every pair of distinct primes; the single counter-example 3 - 2 = 1 alone rules out both fixed claims, since 1 is neither prime nor composite.

Therefore neither of the fixed characterizations offered holds in general, so the correct choice is None of the mentioned.