perfect numbers < 10⁴ are Euclid’s four
Theorem.perfect numbers < 10⁴ are Euclid’s four — the complete sweep finds exactly {6, 28, 496, 8128} = 2^(p−1)(2^p−1) for prime Mersennes p = 2,3,5,7.
Proof.the complete sweep finds exactly {6, 28, 496, 8128} = 2^(p−1)(2^p−1) for prime Mersennes p = 2,3,5,7 — Euler converse cited; odd perfect existence stays OPEN.
The domain is finite and every case is decided by exact arithmetic, so the enumeration is complete. ∎
src/thunder/waves/index.ts#discoveredTheoremsWaveTwo
1 · Classification
finite-complete — computed witness within a cited frame (the unbounded form leans on the cited literature)
2 · Provenance
Documented theorem re-derived by exhaustive computation (humanityNovel=false); first-in-this-registry is the only sense of discovered.
Acknowledgment
"perfect numbers < 10⁴ are Euclid’s four" 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 discoveredTheoremsWaveTwo.
- 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 (discoveredTheoremsWaveTwo @ src/thunder/waves) 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 discoveredTheoremsWaveTwo (src/thunder/waves/index.ts) — every verdict re-derives; nothing on this page is asserted without the computation behind it.