Owlet puzzle #14
Released Sunday, July 19, 2026 UTC
65537
the answer for puzzle #14
The five clues
- A five-digit prime just above sixty-five thousand.
- A prime such that (prime − 1) is a power of two.
- The fifth (and largest known) Fermat prime.
- Constructed as 2 raised to a power of 2, plus 1.
- Gauss proved the regular 65537-gon is constructible with compass and straightedge.
Backstory
F₄ = 65537 is prime; F₅ through F₃₂ are all composite. Only five known Fermat primes: 3, 5, 17, 257, 65537. Gauss proved that a regular n-gon is constructible with compass and straightedge iff n has only Fermat primes among its odd prime factors.
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