Pierre Fermat thought if you square 2 a number of times and add
1, you get a prime:
2 + 1 = 3 The zeroth Fermat number (2 squared zero times)
22 + 1 = 5 The 1st Fermat number (2 squared 1 time)
(22)2 + 1 = 17 The 2nd Fermat number
((22)2)2 + 1 = 257 The 3rd Fermat number
(((22)2)2)2 + 1 = 65537 The 4th Fermat number