How Euler Factored 4294967297 (and Other Massive Numbers)

In the 1630s, Fermat conjectured that 2^2^n+1 was always prime, although he didn't have the tools -- or the patience -- to check beyond the first 5 examples. In this video, we explore how Euler managed to disprove that conjecture, and find some other crazy factorizations in the process.