Euclid’s construction of perfect numbers
Theorem.Euclid’s construction of perfect numbers — a Mersenne prime 2^p−1 gives the perfect number 2^{p−1}(2^p−1) with σ=2N.
Proof.a Mersenne prime 2^p−1 gives the perfect number 2^{p−1}(2^p−1) with σ=2N — verified for p=2,3,5,7 → 6, 28, 496, 8128.
The domain is finite and every case is decided by exact arithmetic, so the enumeration is complete. ∎
src/4/6/index.ts#discoveredTheoremsWaveFiftyFive
1 · Classification
finite-complete — self-contained computation, no external lean
2 · Provenance
Documented theorem re-derived by exhaustive computation (humanityNovel=false); first-in-this-registry is the only sense of discovered.
Acknowledgment
"Euclid’s construction of perfect numbers" is a re-derivation, acknowledged to documented mathematics — the original proof is the prior art this re-derivation acknowledges; not new to humanity — the contribution is the reproducible computation discoveredTheoremsWaveFiftyFive.
- Prior art
- documented mathematics — the original proof is the prior art this re-derivation acknowledges
- Novelty
- not new to humanity — a re-derivation (humanityNovel = false)
- Contribution
- a reproducible computation (discoveredTheoremsWaveFiftyFive @ src/4/6) that re-derives the result at zero tokens — the contribution is the verifiable recomputation, NOT the theorem
3 · Reproducibility
Recompute from source: npm run theorems:verify recomputes discoveredTheoremsWaveFiftyFive (src/4/6/index.ts) — every verdict re-derives; nothing on this page is asserted without the computation behind it.