History of Primes, due on October 14

I was a little late, but I was walking in while the Dr. Friedlander was being introduced.

1. (Difficult) Much of what we learned was review from class, but not all.  It was interesting looking at the same ideas with slightly different formulas.  For example, I think he expressed something like a^ϕ(n) - 1 is divisible by n for Euler's Theorom.  We've thought of it more as a^ϕ(n) is congruent to 1, mod n.  But the idea's the same.  I suppose it was a bit difficult to understand some new concepts, like Mersenne primes, but I think with effort I could (probably because he was trying to make the lecture understandable to those of varying backgrounds).
2. (Reflective) I was hoping for a little more of a history lecture.  With people and dates associated with development and uses of prime number theory.  It was a math colloquium though, not a history one, and I was impressed with the amount of historical context provided.  Now that I know some applications of primes in the field of cryptography, I would be interested to know if there are other areas that use some of these interesting historical ideas.  I wonder what drove these early thinkers to think so much about primes?  Did they have some practical application in mind, or did they feel inspired for other reasons to do their work?
   Also, I think the way he explained the Euclidean helped me gain slightly better intuition into why it works.  I don't remember exactly what he said, but I think part of it was something about the remainder and the result of the division share the GCD all the way down the chain.