There are many definitions of prime numbers—and they all mean the same thing in translation. For example, prime numbers are defined as positive integers (natural numbers) that are greater than 1 and have only 1 and the prime number as divisors (factors). Another definition is an integer greater than 1, in which its only positive divisors are 1 and itself. Still yet another definition is that a prime is a natural number that has exactly two distinct natural number divisors, 1 and itself. For instance, the prime numbers less than 20 are 2, 3, 5, 7, 11, 13, 17, and 19. All other integers greater than 1 that are not prime numbers are called composite numbers.

There are other rules concerning prime and composite numbers. The number 1 is unique, and is not considered a prime or composite number. And one of the basic theorems of arithmetic is that any positive integer is either a prime or the product of a unique set of prime numbers. For example, the number 12 is not a prime, but it has a unique “prime calculation” written as: 2 × 2 × 3.