Fermat number F₅ is composite
Theorem.Fermat number F₅ is composite — F₅ = 2^{2⁵} + 1 = 4 294 967 297 = 641 × 6 700 417.
Proof.F₀..F₄ are prime but F₅ = 2³² + 1 = 4294967297 = 641 × 6700417 exact in BigInt — Euler’s 1732 refutation of Fermat’s "all F_n prime" conjecture, recomputed.
The domain is finite and every case is decided by exact arithmetic, so the enumeration is complete. ∎
src/9/1/index.ts#discoveredTheoremsWaveTwentyFour
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
"Fermat number F₅ is composite" 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 discoveredTheoremsWaveTwentyFour.
- 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 (discoveredTheoremsWaveTwentyFour @ src/9/1) 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 discoveredTheoremsWaveTwentyFour (src/9/1/index.ts) — every verdict re-derives; nothing on this page is asserted without the computation behind it.