Six, taken apart
The counterpart witness: composites exist too. 6 is the smallest number that is a product of two DIFFERENT primes, which is exactly why it later stars in counterexamples (like showing composites fail Euclid's lemma).
A two-brick LEGO assembly next to the single bricks 2 and 3.
6 = 2 × 3. Divisors: 1, 2, 3, 6 — more than just {1, 6}, so not prime.
Concrete composites are the test cases against which prime-only properties (like Euclid's lemma) are sharpened.
Level 1 The precise statement
6 is composite: 6 = 2 * 3, so it has a divisor other than 1 and 6.
Level 3 What it stands on (1 direct)
- Integers form a commutative ring (axiom)
- Divisibility (definition)
- Prime number (definition)
- Composite number (definition)
- 6 is composite (example)
Level 4 The verified record
This page is generated from a machine-checked node. The kernel confirms its dependencies resolve, nothing is circular, and it grounds in axioms (foundation: peano). The content hash below makes tampering evident.
Nothing yet — this is a frontier result.
Nothing depends on it yet, so its failure would be contained.