I was torn between posting a video explanation of how they found the recent super-massive Mersenne Prime and this shorter bit on Lucas Numbers, which is how they found it. Since this video has more explanation–and some very cool commentary on the nature of mathematics toward the end–I went with it. I’ll save the super-Mersenne for another day.
Lucas Numbers are related to the Fibonacci Sequence. Both are related to the Golden Ratio, which I definitely need to post on at some point. Like many Numberphile videos, this one does a good job conveying infectious love of numbers. Enjoy!