State/Natural numbers are prime or composite or zero or one

Logical Connections

This statement logically relies on the following definitions and statements: Def/Prime number, Def/Composite number

The following statements and definitions rely on the material of this page: State/Natural numbers can be factored into primes

To visualize the logical connections between this statements and other items of mathematical knowledge, you can visit the following cluster(s), and click the "Visualize" tab: Clust/Basic number theory

The desired classification follows logically from the following four statements:

• $0$ and $1$ are not prime numbers.
• $0$ and $1$ are not composite numbers.
• No number is both prime and composite.
• Every natural number $n$, which satisfies $n > 1$, is either prime or is composite.