prime numbers

A prime number is a whole number greater than \(1\) that has exactly two divisors: \(1\) and itself. This means it cannot be formed by multiplying two smaller whole numbers.

Key Rules

• Only two factors: Divisible only by \(1\) and the number itself (e.g., \(13\) is divisible only by \(1\) and \(13\)).

• The number \(1\): Is not a prime number. It only has one divisor.

• The number \(2\): Is the first prime number and the only even prime number

Examples

• Prime: \(2, 3, 5, 7, 11, 13, 17, 19, 23, 29...\)

• Not Prime (Composite): Numbers like \(4\) (\(2 \times 2\)) or \(15\) (\(3 \times 5\)) have more than two factors.

Why they matter

Mathematicians consider primes the "building blocks" of all numbers. Under the Fundamental Theorem of Arithmetic, every whole number greater than \(1\) is either prime or can be broken down (factored) into a unique combination of primes. Because of this, they are heavily utilized today to create secure encryption algorithms for computer security and internet privacy.