This class is about the philosophy of math, with a focus on numbers which are only divisible by 1 and themselves (the coolest and most important elements in number theory). We will discuss the following topics: Definition of the fundamental theorem of arithmetic. Proof of there being infinitely many primes. Applications to group theory and cryptography (your computer is using primes right now to look at this webpage). Discussion of the twin prime conjecture and Goldbach's conjecture. Introduction to formal systems and deductive proofs. Outline of Goedel's incompleteness theorem and its relevance to the most important problems in mathematics.