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Owlet puzzle #14

Released Sunday, July 19, 2026 UTC

65537
the answer for puzzle #14

The five clues

  1. A five-digit prime just above sixty-five thousand.
  2. A prime such that (prime − 1) is a power of two.
  3. The fifth (and largest known) Fermat prime.
  4. Constructed as 2 raised to a power of 2, plus 1.
  5. 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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