Observations on a theory of Fermat and others on looking at prime numbers
Euler shows that the fifth Fermat number, 225 +1 = 4,294,967,297, is not prime because it is divisible by 641, though he does not give any clues about how he discovered this fact. He also tacks on a few "theorems" but says that he does not yet know how to prove them.
Original Source Citation
Commentarii academiae scientiarum Petropolitanae, Volume 6, pp. 103-107.
Opera Omnia Citation
Series 1, Volume 2, pp.1-5.