prime number

Also known as prime, 1-almost prime

positive integer with exactly two divisors, 1 and itself

AI overview

A prime number is a positive integer that can only be divided evenly by 1 and itself, such as 2, 3, 5, or 7. Prime numbers are fundamental building blocks in mathematics because every other positive integer can be expressed as a product of primes, making them essential to understanding number structure and important for applications like encryption.

AI-generated from the Wikipedia summary — may contain errors.

Wikidata facts

Subclass of: odd number
Followed by: twin prime
Image: Prime number Cuisenaire rods 7.png

Show 9 more facts

Commons category: Prime numbers
topic's main category: Category:Prime numbers
Stack Exchange tag: math.stackexchange.com/tags/prime-numbers
has characteristic: divisor
opposite of: composite number
has list: list of prime numbers
notation: P/p
on focus list of Wikimedia project: Wikipedia:Vital articles/Level/4
maintained by WikiProject: WikiProject Mathematics

Sources (3)

via Wikidata · CC0

~40 min read

Encyclopedic overview

Composite numbers can be arranged into rectangles but prime numbers cannot.

A prime number (or a prime) 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.

Excerpted from Wikipedia’s “prime number” article, available under the CC BY-SA 4.0 licence.