Owlet puzzle #8
Released Monday, July 13, 2026 UTC
8128
the answer for puzzle #8
The five clues
- A four-digit multiple of one hundred twenty-seven.
- A perfect number.
- The fourth perfect number, of the form 2^(p−1)·(2^p − 1) with p = 7.
- The next perfect number, 33,550,336, has eight digits — perfect numbers grow fast.
- Its divisor sum σ(n) equals 2n exactly.
Backstory
The fourth perfect number, after 6, 28, and 496 — recorded by Nicomachus around 100 AD. 8128 = 2⁶ · (2⁷ − 1) = 64 · 127, matching Euclid's formula with Mersenne prime 127. The next perfect number is 33,550,336.
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