Prime numbers are whole numbers greater than 1 that have exactly two factors: 1 and the number itself. The number 7 is prime because only 1 and 7 divide it with no remainder. The number 8 is not prime because 2 and 4 also divide it. Primes are the building blocks of all whole numbers.
Type any number below to see if it is prime. If it is not, the checker shows its prime factors.
What are prime numbers?
A factor is a number that divides another number exactly. Every whole number above 1 has at least two factors, 1 and itself. If those are the only two, the number is prime. If it has even one more factor, it is composite.
- Prime: 13 has factors 1 and 13 only.
- Composite: 15 has factors 1, 3, 5 and 15.
- Neither: 1 has only one factor, so it is not prime and not composite. 0 is not prime either.
List of prime numbers
The first seven prime numbers are 2, 3, 5, 7, 11, 13 and 17. Here are all the prime numbers from 1 to 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
That is 25 primes below 100. There are 168 prime numbers between 1 and 1000. Primes never run out. A Greek mathematician named Euclid proved long ago that the list of all prime numbers goes on forever. See the full charts on prime numbers 1 to 100 and prime numbers 1 to 1000.
Even prime numbers
There is only one even prime number, and it is 2. Every other even number can be divided by 2, so it has at least three factors: 1, 2 and itself. That means the set of even prime numbers is {2}. Between 1 and 100, and between 1 and 50, the only even prime is still 2. Every other prime is odd, but not every odd number is prime. For example, 9 = 3 × 3 and 21 = 3 × 7.
How to find prime numbers
There is no simple formula that gives every prime. Instead, you test a number by dividing. Here is the easy way:
- If the number is 2, it is prime. If it is any other even number, it is not.
- Find the square root of the number, roughly. For 97, the square root is a little less than 10.
- Divide by each prime up to that square root: 2, 3, 5 and 7 for 97.
- If none of them divide exactly, the number is prime. 97 passes every test, so 97 is prime.
Why stop at the square root? If a number has a factor bigger than its square root, it must also have a partner factor smaller than the square root. So you would already have found it.
A number ending in 0, 2, 4, 6 or 8 is even. A number ending in 0 or 5 divides by 5. If the digits add up to a multiple of 3, the number divides by 3. For example, 51 has digits 5 + 1 = 6, so 51 = 3 × 17 and it is not prime. Watch out for 91. It looks prime, but 91 = 7 × 13. You can check this in the table of 7.
To list all primes in a range, use the Sieve of Eratosthenes. Write the numbers in a grid, then cross out the multiples of 2, 3, 5 and 7 (but not those primes themselves). Whatever is left from 2 to 100 is prime. In a computer program, such as one written in Python or Java, the same idea is used: a loop tries divisors up to the square root.
Prime and composite numbers
A composite number has more than two factors. It can be written as a product of smaller primes. From 1 to 100 there are 25 prime numbers and 74 composite numbers. The number 1 is the one left over, since it is neither.
| Point | Prime number | Composite number |
|---|---|---|
| Number of factors | Exactly 2 | More than 2 |
| Smallest | 2 | 4 |
| Even examples | Only 2 | 4, 6, 8, 10, 12 |
| Odd examples | 3, 5, 7, 11, 13 | 9, 15, 21, 25, 27 |
| Can be split | No, only 1 × itself | Yes, 12 = 2 × 2 × 3 |
So every whole number from 2 upward is either prime or composite, and odd or even. That gives four groups: odd primes (like 3), the even prime 2, odd composites (like 9) and even composites (like 4).
Practice questions with answers
- All prime numbers between 20 and 40: 23, 29, 31 and 37.
- Average of all prime numbers between 30 and 50: the primes are 31, 37, 41, 43 and 47. Their sum is 199, so the average is 199 ÷ 5 = 39.8.
- Is 57 prime? No. 5 + 7 = 12, which divides by 3, and 57 = 3 × 19.
- Is 89 prime? Yes. It does not divide by 2, 3, 5 or 7.
Want more? Learn about twin prime numbers, which are primes 2 apart, and co-prime numbers, which share no common factor except 1. You can also see how to write 97 in words, the largest prime below 100.
Questions people ask
What are prime numbers?
Prime numbers are whole numbers greater than 1 with exactly two factors, 1 and the number itself. Examples are 2, 3, 5, 7, 11 and 13. Numbers with more factors are called composite.
Which is the only even prime number?
The only even prime number is 2. Every other even number divides by 2, so it has more than two factors. That makes 2 the smallest prime and the only even one.
Is 1 a prime number?
No. A prime must have exactly two different factors, and 1 has only one factor, itself. So 1 is neither prime nor composite.
What is the difference between prime and composite numbers?
A prime number has exactly two factors. A composite number has more than two factors, so it can be written as a product of smaller primes. For example, 11 is prime while 12 = 2 × 2 × 3 is composite.
How to find prime numbers easily?
Divide the number by each prime up to its square root. If none divide exactly, the number is prime. For numbers up to 100, you only need to test 2, 3, 5 and 7.