What Is a Prime Number?
A prime number is a whole number greater than 1 that has exactly two factors: 1 and itself.
- 7 is prime: its only factors are 1 and 7
- 12 is not prime: its factors are 1, 2, 3, 4, 6, and 12 — too many
- 2 is prime: its only factors are 1 and 2 (and it is the only even prime)
A number that is not prime (and is greater than 1) is called composite. Composite numbers can be divided evenly by numbers other than 1 and themselves.
The first prime numbers
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47...
Notice: there is no pattern or formula for predicting primes. They are distributed irregularly among the whole numbers. This is part of what makes them fascinating to mathematicians.
Why is 1 not prime?
This is the most common confusion. 1 has only one factor (itself). Prime numbers must have exactly two factors — 1 and the number itself. Since 1 has only one factor, it does not qualify.
This is not arbitrary. If 1 were prime, the Fundamental Theorem of Arithmetic (every number has a unique prime factorization) would break: 12 could be written as 2 × 2 × 3, or 1 × 2 × 2 × 3, or 1 × 1 × 2 × 2 × 3. Excluding 1 keeps factorization unique.
How to test if a number is prime
To check if a number is prime, try dividing it by all primes up to its square root:
Is 29 prime? √29 ≈ 5.4. Check: 29 ÷ 2? No. 29 ÷ 3? No. 29 ÷ 5? No. No prime up to 5 divides 29 evenly, so 29 is prime.
Is 51 prime? √51 ≈ 7.1. Check: 51 ÷ 2? No. 51 ÷ 3? Yes (51 = 3 × 17). So 51 is composite.
Why prime numbers matter
Primes are the building blocks of all whole numbers. Every whole number greater than 1 is either prime or can be written as a product of primes:
- 12 = 2 × 2 × 3
- 30 = 2 × 3 × 5
- 100 = 2 × 2 × 5 × 5
This is called prime factorization, and it is used in finding GCF and LCM, simplifying fractions, and — in advanced applications — computer encryption that keeps the internet secure.
Related concepts
- Factors and multiples: primes are numbers with exactly two factors
- Multiplication facts: prime factorization builds on multiplication fluency
- Equivalent fractions: simplifying fractions uses prime factors