What is the name for a number that is divisible by only 1 and itself?

A number divisible only by 1 and itself is called a prime number. In standard mathematics, a prime is a natural number greater than 1 with exactly two positive divisors: 1 and the number itself.

Examples include 2, 3, 5, 7, and 11. The number 2 is especially notable because it is the only even prime; every other even number is divisible by 2 and therefore has more than two positive divisors. By contrast, 4 is composite because it can be divided evenly by 1, 2, and 4.

A common mix-up concerns the number 1. It is not prime because it has only one positive divisor, not two. Prime numbers are the basic building blocks of whole-number arithmetic: the fundamental theorem of arithmetic says every integer greater than 1 can be expressed as a unique product of primes, apart from the order of the factors. This principle underlies factoring, number theory, and much of modern cryptography.