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 primes are 2, 3, 5, 7, 11, and 13, and they are the building blocks of every other whole number.
- A prime has exactly two divisors: 1 and itself.
- 1 is not prime — it has only one divisor.
- 2 is the only even prime number.
- A whole number above 1 that is not prime is called composite.
What makes a number prime
Factors are the whole numbers that divide into a number with no remainder. The number 7 can only be divided evenly by 1 and 7, so it has exactly two factors and is prime. The number 8 divides evenly by 1, 2, 4, and 8 — four factors — so it is composite. The test is simple: if a number above 1 has any factor other than 1 and itself, it is not prime.
Why 1 is not a prime number
By definition a prime needs exactly two distinct factors. The number 1 has only one factor (itself), so it fails the test. Excluding 1 also keeps an important rule clean: every whole number above 1 has one unique prime factorization. If 1 counted as prime, you could multiply by 1 endlessly and that uniqueness would break.
Is 2 really prime?
Yes. The number 2 has exactly two factors, 1 and 2, so it meets the definition. It is the only even prime, because every other even number is also divisible by 2 and therefore has at least three factors.
How to check if a number is prime
Use trial division. To test a number n, check whether any whole number from 2 up to the square root of n divides it evenly. If none do, n is prime. You only need to go up to the square root because a larger factor would always pair with a smaller one you have already tested.
Example — is 53 prime? The square root of 53 is about 7.3, so test 2, 3, 5, and 7. None divide 53 evenly, so 53 is prime.
Prime numbers under 100
There are 25 prime numbers below 100:
For a larger printable reference, see the Prime Numbers Chart.
Prime vs composite numbers
| Number | Factors | Type |
|---|---|---|
| 1 | 1 | Neither (unit) |
| 2 | 1, 2 | Prime |
| 9 | 1, 3, 9 | Composite |
| 11 | 1, 11 | Prime |
| 12 | 1, 2, 3, 4, 6, 12 | Composite |
FAQ
What is the smallest prime number? 2 is the smallest prime, and the only even one.
Is 0 a prime number? No. Primes must be greater than 1, so 0 and all negative numbers are excluded.
What is the largest known prime? Primes go on forever (Euclid proved there are infinitely many). The largest ones found so far have tens of millions of digits and are discovered by distributed computing projects.
To test a specific number, use the Prime Number Checker, and to break a number into its prime building blocks, use the Prime Factorization Calculator.