Section 19 due October 19

1. Why is 1 not considered a prime number? it's only divisible by 1 and itself... it just seems to me like it's a prime... maybe I'm misunderstanding something. Also, what important applications does number theory like this have? For example, how has knowing there are infinitely many primes influenced scientific progress? I'm not trying to be facetious, I'm really curious.

2. The concept of infinitely many primes is incredible to me. I've never really thought about it before... but in a sense prime numbers are the only real unique numbers. Like, this section just proved that every number is actually just a product of a bunch of prime numbers. So, the only really unique numbers are primes. They aren't made up of any other numbers. But then to know that there are infinitely many primes... that's crazy. Like, there's infinite possibilities for uniqueness. I feel like I'm having a hard time grasping and/or expressing these thoughts, but suffice it to say it's interesting to think about.