I did read very carefully with a group of undergraduates the article PRIMES is in P by Manindra Agrawal, Neeraj Kayal, Nitin Saxena. It does not require anything above some modular arithmetic and some very basic knowledge of prime numbers, yet is a remarkable paper published in the Annals.

It gives the students the possibility to see some algebra and some arithmetic applied to a very important and old problem in mathematics. In my experience both groups of students enjoyed it a lot and, more importantly, learned a lot from the reading.