Prime Number

  • mathematics
    a natural number greater than one that has no factors other than one and itself.
All terms


A prime number is a natural number greater than that has no positive divisors other than and itself. In other words, if a number is prime, it cannot be factored into smaller integers.

The first few prime numbers are , , , , , and . Notice that is the only even prime number, and all other prime numbers are odd.

Prime numbers play a fundamental role in number theory through the fundamental theorem of arithmetic, which states that every natural number greater than is either a prime number itself or can be factored as a unique product of prime numbers, up to their order. In other words, every number is either prime or can be expressed as a product of primes.

For example, the prime factorization of is:

Prime numbers are integral to many areas of mathematics and have important applications in computer science, particularly in cryptography.

Related Terms


A number is a mathematical object used to count, measure, and label. The main types of numbers include natural numbers, whole numbers, integers, rational numbers, real numbers, and complex numbers. Each of these types includes different sets of numbers and has different properties.


An integer is a number that can be written without a fractional or decimal component. It includes the natural numbers (1, 2, 3, ...), zero (0), and the negatives of the natural numbers (-1, -2, -3, ...). The set of all integers is often denoted by the letter Z.