--- ## Definition > [!tldr] Definition > A positive integer $n$ is said to be **composite** if it can be written as $n = ab$ where $a$ and $b$ are positive integers greater than $1$. The positive integer $n$ is said to be **prime** if it is not composite; that is, if it has only two factors, $n$ and $1$. Notes: - Note, the number $1$ is neither prime nor composite; and negative numbers are also neither prime nor composite. - If $n$ is a composite number with $n = ab$, then writing $n = ab$ is called a *factorization* of $n$. Writing a positive integer $n$ as $n = p_1 p_2 p_3 \cdots p_k$ for some [[Natural numbers|natural number]] $k$ where each $p_i$ is prime, is called a *prime factorization*. ## Examples | Number | Prime or composite? | | :-----------: | ----------------------------------------------- | | 2 | Prime | | 3 | Prime | | 4 | Composite, factors into $2 \cdot 2$ | | 5 | Prime | | 6 | Composite, factors into $3 \cdot 2$ | | 7 | Prime | | 8 | Composite, $8 = 2 \cdot 4$ | | 20 | Composite, $20 = 2 \cdot 10$ | | 23 | Prime | | 1012346665879 | Prime | | 1030507050301 | Composite, factors into $1010201 \cdot 1020101$ | ## Resources   Other resources: - [List of primes less than 1000](https://byjus.com/maths/prime-numbers-from-1-to-1000) - [List of four-digit primes](https://t5k.org/curios/index.php)