Why are prime numbers more useful than composite numbers in cryptography?

Answer 1

This question is based on a misunderstanding. Most cryptography is based on numbers that are products of two very large prime numbers. Being the product of two primes means that these numbers are composite - not prime!

Answer 2

Cryptography contains codes which should not be broken further. Since prime numbers not composites cannot be broken down, thus they are used.

Answer 3

The basic idea in cryptography is that if you multiply two large prime numbers together, and give somebody the product, it is very hard to find the original factors.