Primes of form Power of Two plus One/Historical Note

Historical Note on Primes of form Power of Two plus One

In $1640$, Pierre de Fermat wrote to Pierre de Fermat wrote to Bernard Frénicle de Bessy 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 Leonhard Paul Euler, who discovered that $2^{2^5}$ is composite in $1732$.

Sources

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $257$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $257$