561 is the smallest Carmichael number, a composite that fools Fermat: 561 = 3 × 11 × 17 is composite and squarefree, yet a^560 ≡ 1 mod 561 for every a coprime to 561 — so Fermat's primality test cannot tell it from a prime. By Korselt's criterion this holds because (p−1) divides 560 for each prime factor p (2, 10, 16 all divide 560); and no composite below 561 has this property. Verified by full enumeration
ab3e7c0b-4a21-8c31-a6a2-23155325ebb2Type anything and watch its uuidna recompute — deterministic, reproducible by anyone, no key. A theorem is alive when you interact with it. A content-address proves integrity, not truth. 0/7.
- theorem key ·
five_six_one_is_the_smallest_carmichael_number - content-address (receipt) ·
109b8dc3-b6f7-8b36-ac72-8d0b91563fa0 - status · decidable, re-verified on every build — recomputes from
src/
The 7D rosetta-ray vortex is plotted from this theorem's microdata (its content-address); the slowly rotating hero background is computed from its seven surrounding theorems' hues — the mesh, seen locally, in analog rotation of dimensions. Each object is the hero of its own page: this theorem at the centre, its neighbours as the field.
How it was achieved
This theorem was computed by exhaustion over a finite domain in scripts/discover.ts — a test: () => boolean that runs to completion, holding by full enumeration. It was gate-checked (its name and content hold the honesty floor — no over-reach), receipted and chained append-only, and it is re-verified on every build: if it ever stopped holding, the build would fail, not production. That is what achieved means here — not asserted, but recomputable.
One leaf of the chained ledger: all theorems · computed results · the guide · the source formula. The repo and the site cross-link both ways — this hero page points back to the formula that recomputes it. Verify by cloning and running npm run lean-claims. A content-address proves integrity, not truth. entails → 0/7.