Owlet puzzle #5
Released Friday, July 10, 2026 UTC
561
the answer for puzzle #5
The five clues
- A three-digit odd number.
- It is not prime, yet passes Fermat's compositeness test for every base coprime to it.
- It is a squarefree product of three primes.
- Its prime factorization is 3·11·17.
- The smallest Carmichael number.
Backstory
561 = 3 · 11 · 17 is the first Carmichael number — a composite that satisfies Fermat's little theorem for every base coprime to it (Korselt's criterion: (p−1) | 560 for each prime factor p). Alford, Granville, and Pomerance proved in 1994 that infinitely many Carmichael numbers exist.
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