What Are Prime Numbers?

A prime number is a whole number greater than 1 that has exactly two factors: 1 and itself. You cannot divide a prime number evenly by any other whole number.

The first ten prime numbers are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29.

Prime numbers are contrasted with composite numbers, which have more than two factors. The number 1 is a special case - it is neither prime nor composite.

Prime vs. Composite

7: 1, 7 - Prime

9: 1, 3, 9 - Composite

11: 1, 11 - Prime

12: 1, 2, 3, 4, 6, 12 - Composite

1: 1 - Neither

The Sieve of Eratosthenes

The Sieve of Eratosthenes (named after the ancient Greek mathematician) is the classic classroom tool for identifying primes:

Write numbers 1–100 on a grid.
Cross out 1 (neither prime nor composite).
Circle 2, then cross out all multiples of 2.
Circle 3, then cross out all multiples of 3.
Circle 5, cross out multiples of 5. Circle 7, cross out multiples of 7.
All remaining uncrossed numbers are prime.

There are 25 prime numbers between 1 and 100.

What Grade Do Kids Learn Prime Numbers?

4th grade (4.OA.B.4): This is the primary grade. Students determine whether a whole number in the range 1–100 is prime or composite. They build on their understanding of factors from earlier in 4th grade.

5th grade and beyond: Prime factorization extends the concept - any composite number can be broken down into a product of prime numbers (e.g., 12 = 2 × 2 × 3).

Common Misconceptions

All odd numbers are prime: This is false. Many odd numbers (9, 15, 21, 25...) are composite. Students should always test for factors rather than relying on even/odd status.

2 is not prime because it's even: Students sometimes exclude 2 from the prime list. In fact, 2 is the only even prime and a very important one.

Larger numbers are more likely to be prime: There's no simple size rule. Primeness depends entirely on factors, not magnitude.

Practice Activities

Sieve coloring: Complete the Sieve of Eratosthenes on a 100 chart with colored pencils.
Prime or composite sort: Cards with numbers 2–50; students sort into two labeled columns.
Factor lists: For each number 2–30, students list all factors and mark whether prime or composite.
Prime detective: Give a large number (like 97 or 101) and have students determine if it is prime by testing divisibility rules.
Prime factorization trees: Draw factor trees for composite numbers and circle the prime factors at the bottom.

Frequently Asked Questions

What is a prime number?

A prime number is a whole number greater than 1 that can only be divided evenly by 1 and itself. For example, 7 is prime because its only factors are 1 and 7. The number 6 is not prime because it can also be divided by 2 and 3.

What is a composite number?

A composite number is a whole number greater than 1 that has more than two factors. For example, 12 is composite because its factors are 1, 2, 3, 4, 6, and 12. Every even number greater than 2 is composite, and many odd numbers are composite as well.

Is 2 a prime number?

Yes - 2 is the only even prime number. Its only factors are 1 and 2. All other even numbers are divisible by 2, giving them at least three factors, so no other even number can be prime.

Why is 1 not considered a prime number?

The number 1 has only one factor (itself), not two. Prime numbers are defined as having exactly two distinct factors. Including 1 as prime would break the Fundamental Theorem of Arithmetic, which says every number has a unique prime factorization.

What is the Sieve of Eratosthenes?

The Sieve of Eratosthenes is an ancient algorithm for finding all prime numbers up to a given limit. Start with a 100 chart: cross out 1 (not prime), circle 2, then cross out all multiples of 2. Circle the next unmarked number (3), cross out its multiples. Repeat for 5, 7, and so on. Numbers that remain circled are prime.