I am currently writing a math paper regarding the importance of prime numbers in RSA encryption. I understand that generating q x p = N (where p and q are prime numbers) is simple for a computer however factoring N into its two primes is improbable within a reasonable amount of time.
As mentioned before I am addressing the importance of prime numbers. What I think the reason for their importance is that if RSA used composite numbers they can be broken up into smaller numbers as they are composite making it easier to factor however I am unsure if this is correct reasoning.
I would greatly appreciate it if someone could help me understand the true importance of prime numbers beyond the simple reasoning that it is because factoring N is highly improbable in a reasonable amount of time.