Numbers built from smaller pieces
Every number greater than 1 is exactly one of two things: prime (an atom) or composite (a molecule). 15 is composite because 3 × 5 builds it. The definition is deliberately just 'not prime' — the two notions are complementary.
If primes are LEGO bricks, composites are the things you snap together from them.
6 = 2 × 3 → composite. 49 = 7 × 7 → composite. 47 → no smaller factors → prime, not composite. 1 → neither (too small by definition).
Factoring composites into primes is the 'hard direction' that cryptography exploits, and detecting compositeness fast is a workhorse of computer algebra.
Level 1 The precise statement
An integer n > 1 is composite iff it is not prime.
Level 3 What it stands on (1 direct)
- Integers form a commutative ring (axiom)
- Divisibility (definition)
- Prime number (definition)
- Composite number (definition)
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.
1 downstream result would collapse with it. See the blast radius on the graph →