A prime number is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways of writing it as a product, 1 × 5 or 5 × 1, involve 5 itself. However, 4 is composite because it is a product (2 × 2) in which both numbers are smaller than 4. Primes are central in number theory because of the fundamental theorem of arithmetic: every natural number greater than 1 is either a prime itself or can be factorized as a product of primes that is unique up to their order.
The Rhind Mathematical Papyrus
The small gear in this piece of farm equipment has 13 teeth, a prime number, and the middle gear has 21, relatively prime to 13.
In mathematics, the natural numbers are the numbers 0, 1, 2, 3, etc., possibly excluding 0.[under discussion] Some define the natural numbers as the non-negative integers 0, 1, 2, 3, ..., while others define them as the positive integers 1, 2, 3, .... Some authors acknowledge both definitions whenever convenient. Some texts define the whole numbers as the natural numbers together with zero, excluding zero from the natural numbers, while in other writings, the whole numbers refer to all of the integers. The counting numbers refer to the natural numbers in common language, particularly in primary school education, and are similarly ambiguous although typically exclude zero.
The Ishango bone (on exhibition at the Royal Belgian Institute of Natural Sciences) is believed to have been used 20,000 years ago for natural number arithmetic.