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Owlet puzzle #18

Released Thursday, July 23, 2026 UTC

1093
the answer for puzzle #18

The five clues

  1. A four-digit prime below 1500.
  2. A prime that fails a strong congruence test involving 2 modulo its own square.
  3. A Wieferich prime: it satisfies 2^(p−1) ≡ 1 (mod p²).
  4. 1093 and 3511 are the only Wieferich primes below 6.7 × 10¹⁵.
  5. First Wieferich prime, found by Meissner in 1913.

Backstory

1093 is the smaller of only two known Wieferich primes (the other is 3511), satisfying 2^(p−1) ≡ 1 (mod p²). These are central to Fermat's Last Theorem's first-case criterion, and no others have been found below 10¹⁷.

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