561 is the smallest Carmichael number
Theorem.561 is the smallest Carmichael number — composite (3·11·17) yet a^(n−1) ≡ 1 (mod 561).
Proof.composite (3·11·17) yet a^(n−1) ≡ 1 (mod 561) for EVERY a coprime to it — a Fermat pseudoprime to all coprime bases, minimality by full sweep; the reason the Fermat primality test can be fooled.
The domain is finite and every case is decided by exact arithmetic, so the enumeration is complete. ∎
src/9/1/index.ts#discoveredTheoremsWaveThirtyOne
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
"561 is the smallest Carmichael number" 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 discoveredTheoremsWaveThirtyOne.
- 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 (discoveredTheoremsWaveThirtyOne @ 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 discoveredTheoremsWaveThirtyOne (src/9/1/index.ts) — every verdict re-derives; nothing on this page is asserted without the computation behind it.