What is a prime number? Definition, examples.

Prime numbers definition

  • Positive integers larger than 1 that are only dividing by 1 and themselves are called prime numbers.
  • Positive integers that have at least one positive divisor (factor) other than 1 and the number itself are called composite numbers.
    A prime number is also any positive integer larger than 1 that is not a composite number.

Examples of prime numbers. Examples of numbers that are not prime.

  • 1 is not considered prime, so the first prime number is 2 (prime numbers list starts by 2);
  • 2 is divisible only by 2 and 1, so 2 is a prime number;
  • 3 is divisible only by 3 and 1, so 3 is a prime number;
  • 4 is divisible by 4, 2 and 1, so 4 is NOT a prime number;
  • 5 is divisible only by 5 and 1, so 5 is a prime number;
  • 7 is divisible only by 7 and 1, so 7 is a prime number;
  • 11 is divisible only by 11 and 1, so 11 is a prime number;
  • 12 is divisible by 12, 6, 4, 3, 2 and 1, so 12 is NOT a prime number;
  • 13 is divisible only by 13 and 1, so 13 is a prime number;

The prime numbers, up to 100:

Why is 1 not a prime number?

Composite numbers are all the positive integers larger than 1 that are not prime numbers. A composite number has at least one positive divisor other than 1 and the number itself.

EUCLID (300 B.C.) proved that as the set of natural or integer numbers is infinite, also the the set of prime numbers is infinite, with no largest prime number.

There is no known simple formula that sets all of the prime numbers apart from composites.


What is a prime number?

What is a composite number?

Prime numbers up to 1,000

Prime numbers up to 10,000

Sieve of Eratosthenes

Euclid's algorithm

Simplifying ordinary (common) math fractions (reducing to lower terms): steps to follow and examples