Mathmatics

Definition of a Prime Number

• A prime number is a whole number greater than $1$ that has exactly two distinct positive factors: $1$ and itself.

• A composite number is a whole number greater than $1$ that has more than two factors.

Key Properties

• Smallest Prime: The number $2$ is the smallest prime number and the only even prime number.

• The Number 1: The number $1$ is neither prime nor composite because it only has one factor ($1$).

Examples and Analysis

• Prime Examples:

  • $2$ (factors: $1$, $2$)

  • $3$ (factors: $1$, $3$)

  • $5$ (factors: $1$, $5$)

  • $7$ (factors: $1$, $7$)

  • $71$ (factors: $1$, $71$)

• Non-Example (Composite Number):

  • $72$ is composite, not prime, because it has factors other than $1$ and itself: $1$, $2$, $3$, $4$, $6$, $8$, $9$, $12$, $18$, $24$, $36$, and $72$.