What Are Prime Numbers? How to Spot Them
Learn what prime numbers are, how to spot them, and see a list of the smaller primes. Includes why 1 is not prime and how primes connect to prime factorization.
Prime numbers are a basic idea in middle-school math. This guide explains what a prime number is, how to spot one, and lists the smaller primes.
What is a prime number?
A prime number is a whole number greater than 1 that can be divided evenly only by 1 and itself. In other words, it has exactly two divisors: 1 and itself. For example, 7 can only be divided by 1 and 7, so it is prime.
By contrast, 6 can be divided by 1, 2, 3, and 6 (four divisors), so it is not prime. A whole number greater than 1 that is not prime is called a composite number.
Why 1 is not prime
A common misconception is that 1 is prime. But 1 has only one divisor (itself), so it does not meet the rule of having exactly two divisors. That is why 1 is not prime. In prime factorization, too, we never divide by 1, so it helps to remember this.
A list of small primes and how to spot them
The primes up to 50 are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, and 47 — fifteen in all. Two is the only even prime; every other prime is odd.
To check whether a number is prime, try dividing it by the primes up to about its square root. If none divide it evenly, it is prime. For example, 97 is not divisible by 2, 3, 5, or 7, and the square of the next prime, 11 (which is 121), is already larger than 97, so 97 is prime.
Related topics and tools
Primes are the building blocks of prime factorization. Breaking a number into a product of primes helps with greatest common divisors, least common multiples, and simplifying fractions. The prime factorization calculator also includes a prime check, so try entering a number you are curious about.