Primes of form Power of Two plus One/Historical Note

Historical Note on Primes of form Power of Two plus One
In $1640$, wrote to  wrote to  announcing this result.

From the fact that all integers of the form $2^n + 1$ such that $n = 2^k$ that he tested were prime, he went on to make his famous Fermat Prime Conjecture: that they are all prime.

This was refuted by, who discovered that $2^{2^5}$ is composite in $1732$.