Pure mathematics exists to study abstract concepts with no consideration given to their practical applications. Applied mathematicians and scientists in a wide variety of disciplines then draw on the discoveries of the pure mathematicians and apply them to their own particular areas of expertise. There is no pressing need for teachers to justify and demonstrate to students how mathematics can be useful in the "real world". Quite the opposite, teachers should convey to their students that pure mathematics is at the heart of mathematics. It is a sublime and purely mental world that is not tied to the physical world in any way. To focus on the usefulness of mathematics is to mar this intrinsic beauty. Sure, prime numbers are used in cryptography but prime numbers have always fascinated the greatest mathematicians. The problem faced by students in high school mathematics is that this sense of wonder and fascination in mathematical concepts like prime numbers is missing. It's often lacking in their teachers in the first place.