Prime Numbers: Definition, List and How to Find Them
Part of the Math Concepts guide for Grades 3 to 8.
If your child is working through prime numbers in class, this page covers what they need in one place: the definition, the full list to 100, and a simple method for checking any number yourself. It pairs well with our guide on integers if that's the next concept on their homework.
What Is a Prime Number?
A prime number is a whole number greater than 1 that has exactly two factors: 1 and itself. It cannot be divided evenly by any other whole number. The first five prime numbers are 2, 3, 5, 7, and 11. A composite number is a whole number with more than two factors. The number 1 is neither prime nor composite; it sits in its own special category.
Prime vs. Composite Numbers
| Number | Prime or Composite? | Why |
|---|---|---|
| 1 | Neither | Has only one factor: itself |
| 2 | Prime | Factors: 1 and 2 only. The only even prime number. |
| 3 | Prime | Factors: 1 and 3 only |
| 4 | Composite | Factors: 1, 2, 4 |
| 5 | Prime | Factors: 1 and 5 only |
| 6 | Composite | Factors: 1, 2, 3, 6 |
Prime Numbers from 1 to 100
There are 25 prime numbers between 1 and 100:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97
A few things worth pointing out to students:
- 2 is the only even prime. Every other even number has 2 as a factor, so none of them can be prime.
- All prime numbers except 2 are odd.
- No prime number ends in 5 (except 5 itself), because any number ending in 5 is divisible by 5.
- Primes become less frequent as numbers get larger.
How to Tell If a Number Is Prime
The simplest method is called trial division. Here is how to use it step by step.
| Step | What to check | Result |
|---|---|---|
| 1 | Is the number less than 2? | If yes, it is not prime |
| 2 | Is it 2 or 3? | If yes, it is prime |
| 3 | Is it even (divisible by 2)? | If yes, it is not prime |
| 4 | Try dividing by odd numbers: 3, 5, 7... | Only test up to the square root of the number |
| 5 | No divisors found? | The number is prime |
Example: Is 37 Prime?
- Find the square root of 37. It is approximately 6.1, so we only need to test primes up to 6: that means 2, 3, and 5.
- 37 divided by 2 = 18.5. Not a whole number, so 2 is not a factor.
- 37 divided by 3 = 12.3. Not a whole number, so 3 is not a factor.
- 37 divided by 5 = 7.4. Not a whole number, so 5 is not a factor.
- No divisors found, so 37 is prime.
Common Mistakes to Avoid
Mistake 1: Thinking 1 Is a Prime Number
This is the most common mistake students make. By definition, a prime number must have exactly two distinct factors. The number 1 has only one factor, which is itself. Since it does not meet the two-factor requirement, 1 is neither prime nor composite.
Mistake 2: Forgetting That 2 Is Prime
Some students assume all prime numbers are odd, which leads them to skip 2. Remember: 2 is prime because its only factors are 1 and 2. It is the only even prime number.
Mistake 3: Confusing Prime and Composite
A helpful reminder: the word composite means made up of parts. A composite number can be built by multiplying smaller whole numbers together. A prime number cannot be broken down that way.
Why Parents Use Prodigy Alongside Concepts Like This
Consistent Prodigy use throughout the school year has been proven to help students strengthen foundational math understanding and confidence. Among multiple studies commissioned by Prodigy Education. Individual results may vary, results are not guaranteed. Studies may be viewed here: prodigygame.com/main-en/research
"I love watching my child play Prodigy. It is something that not only we can do together, but it allows me to see and understand what he is working on in math." (Samantha Moyer, Parent)
Common Questions About Prime Numbers
What is a prime number?
A prime number is a whole number greater than 1 with exactly two factors: 1 and itself. It cannot be divided evenly by any other number. Examples include 2, 3, 5, 7, 11, and 13.
Is 1 a prime number?
No. The number 1 is not prime. A prime number must have exactly two distinct factors. Since 1 has only one factor, it does not meet that requirement. It is neither prime nor composite.
What is the smallest prime number?
2 is the smallest prime number. It is also the only even prime number. Every other even number has 2 as a factor, giving it at least three factors and making it composite.
What is the difference between prime and composite numbers?
A prime number has exactly two factors: 1 and itself. A composite number has more than two factors and can be divided evenly by numbers other than 1 and itself. The number 1 is neither prime nor composite.
How many prime numbers are there between 1 and 100?
There are 25 prime numbers between 1 and 100: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97.
Why are prime numbers important?
Prime numbers are fundamental in mathematics and cryptography. Every composite number can be expressed as a unique product of prime numbers, which is called prime factorization. Modern internet encryption, including the HTTPS protocol that keeps websites secure, relies on the difficulty of factoring very large numbers into their prime components.
Keep Building Number Sense
Prodigy has been shown to help students build stronger math skills. Among multiple studies commissioned by Prodigy Education. Individual results may vary, results are not guaranteed. Studies may be viewed here: prodigygame.com/main-en/research
"Prodigy is an engaging way to keep your child interested in learning new math skills and facts." (Amber Gouge, Parent)
