In June of 2009, the 47th perfect number was discovered by the Great Internet Mersenne Prime Search (GIMPS), a collaborative computing project involving volunteers from all over the world. Like all known perfect numbers before it, this number is even. Does an odd perfect number exist? Are there infinitely many perfect numbers?
Holdener, Judy, "Perfect and Abundant Numbers - a Perfect and Abundant Source for Undergraduate Research Projects (Abstract)" (2011). Undergraduate Mathematics Day. 17.