Definition:Fermat Number/Historical Note

Historical Note on Fermat Number
observed that the first $5$ numbers of the form $2^{2^n} + 1$ are all prime.

This led him to propose the Fermat Prime Conjecture, that all numbers of this form are prime.

The Fermat Prime Conjecture was proved false by, who discovered the prime decomposition of the $6$th Fermat number.