Some of you asked about further reading about the prime number theorem and 
the Riemann zeta function.   

I looked at my own bookcase, and found 4 books:

1) Number theory and its history - by Oystein Ore

Not as rigorous as I hope, like omitting gcd(0,0) but certainly the most
accessible of the 4.  It is an expanded version of our Chapters 2-3, with
plenty of cute little questions that can be used for our class.  Not much of
the prime number theorem nor the Riemann zeta fcn.

2) The little book of the big primes - by Paulo Ribenboim

The level of rigor is similar to our class, proofs are given when cute ones
exist, and omitted when they are a burden.  It discusses many fun things
about primes without much difficult background.  There are good discussions
of both \pi and \zeta, no proof of prime number theorem.

3) Elementary number theory - by Gareth A. Jones and J. Mary Jones

2.5 times thicker, still elementary (so accessible for 1st-2nd year
students) and besides \pi and \zeta, there is a chapter on Fermat's last
theorem (one more on quadratic residues, one on sums of squares, and
appendices on well-order principles and groups etc).

4) Introduction to Analytic Number Theorey - by Tom Apostol

2 proofs of the prime number theorem, and one chapter on partitions. This is
still a "UTM" of the Springer series, and has intentionally been toned down
to be accessible, but it is the kind of book to be read quietly when you're
energetic.

The prices are around 20, 20, 40, 50, and of course, the library may have 
some copies. 

I think 2) and 3) are better starting points.  4) can be done,
say, over a more relaxed summer.

Incidentally,

 http://en.wikipedia.org/wiki/Riemann_zeta_function

is nice in its own way.  No proofs, but the best part is that, every terminology
can be learnt with a click.