There shouldn't be a direct association, are you referring to something specific? Choosing a good password is about making it less predictable.

Prime numbers do factor into cryptography though, they use prime numbers for key generation and key exchange.

I'm more curious as to why prime numbers are so important to encryption, like what is their role or significance to the process

But don't use a prime number as your password ;-)

Do passwords eventually break down into some simpler representation tho? Like doesn't some hash function convert it irreversibly into some other number?

there is no such thing as a good password. I have heard of good SSO's though

WHO hurt you :[