Definition:Fermat Number/Historical Note

Historical Note on Fermat Number
In $1640$, wrote to  that $2^n + 1$ is composite if $n$ is divisible by an odd prime.

He also 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.

On being unable to prove it, he sent the problem to, with the note:
 * I wouldn't ask you to work at it if I had been successful.

Pascal unfortunately did not take up the challenge.

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