Prime number

A prime number is a natural number greater than 1 whose only factors are 1 and the number itself. A number greater than 1 that has other factors too is a composite number.

• The smallest primes. \(2, 3, 5, 7, 11, 13, 17, 19, 23, 29, \dots\) There are infinitely many primes.
• Building blocks. Every natural number greater than 1 is a product of primes, and apart from their order the factors are always the same: \(90 = 2 \cdot 3^2 \cdot 5\).
• Testing. It is enough to try dividing by the primes whose square is not greater than the number. For example, 97 is not divisible by 2, 3, 5 or 7, and \(11^2 = 121 \gt 97\), so 97 is prime.