Prime Number
A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. The first few primes are 2, 3, 5, 7, 11, and 13. By definition, 1 is not considered prime. The number 2 is the only even prime; all other primes are odd.
Fundamental Role in Mathematics
Every integer greater than 1 either is prime or can be expressed as a product of primes in a unique way. This result, known as the Fundamental Theorem of Arithmetic, establishes primes as the basic multiplicative building blocks of the natural numbers. Because of this property, primes are central to number theory and have applications across mathematics and computer science.
Distribution and Properties
While primes become less frequent as numbers grow larger, there are infinitely many primes. The distribution of primes follows patterns that mathematicians continue to study, including the Prime Number Theorem, which describes their asymptotic density. Testing whether large numbers are prime, and factoring composite numbers into their prime components, forms the basis of modern cryptographic systems.