Which of the following is not a property of prime numbers?

The correct answer is rooted in the fundamental definition of prime numbers. Prime numbers are defined as natural numbers greater than one that have exactly two distinct positive divisors: one and the number itself. This means that a prime number cannot be expressed as the product of other integers, aside from the trivial case of 1 multiplied by the prime number itself. Thus, the statement about being expressible as the product of other integers is not a property of prime numbers, making it the correct choice.

Understanding the properties of prime numbers is essential to grasping concepts in number theory and various areas of mathematics, as primes serve as the building blocks for all integers. The incorrect options detail valid characteristics of prime numbers: they are indeed divisible only by one and themselves, have exactly two distinct positive divisors, and the only even prime is two, since all other even integers can be divided by 2 and thus have more than two divisors.