even perfect numbers come from Mersenne primes (Euclid): when 2^p − 1 is a Mersenne prime, 2^(p−1)·(2^p − 1) is a perfect number — equal to the sum of its proper divisors. So p = 2, 3, 5, 7 (with Mersenne primes 3, 7, 31, 127) give the first four perfect numbers 6, 28, 496, 8128; but p = 11 gives 2^11 − 1 = 2047 = 23 × 89, not prime, and the formula yields no perfect number. Verified by full enumeration of divisors
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 ·
even_perfect_numbers_come_from_mersenne_primes - content-address (receipt) ·
8f5149b4-e512-8102-8fc2-21f94d989be2 - 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.