Prime number

In mathematics, a prime number (or prime) is a natural number greater than one whose only positive divisors are one and itself. Or for short: A prime number is a natural number with exactly two natural divisors. A natural number that is greater than one and is not a prime is called a composite number. The numbers zero and one are neither prime nor composite. The property of being a prime is called primality. Prime numbers are of fundamental importance in number theory.

Related Topics:
Mathematics - Natural number - One - Positive - Divisor - Composite number - Zero - Number theory

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

The sequence of prime numbers begins

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

:2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, ...

Related Topics:
2 - 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23 - 29 - 31 - 37 - 41 - 43 - 47 - 53 - 59 - 61 - 67 - 71 - 73 - 79 - 83 - 89 - 97 - 101 - 103 - 107 - 109 - 113 - ...

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

This is sequence in OEIS; see list of prime numbers for the first 500 primes. The set of all prime numbers is sometimes denoted by ℙ, a blackboard bold P. As 2 is the only even prime number, the term odd prime is used to refer to all prime numbers except 2.

Related Topics:
OEIS - List of prime numbers - Blackboard bold

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

In the context of ring theory, a branch of abstract algebra, the term "prime element" has a specific meaning. Here, a ring element a is defined to be prime if whenever a divides bc for ring elements b and c, then a divides at least one of b or c. With this meaning, the additive inverse of any prime number is also prime. In other words, when considering the set of integers ℤ (Z) as a ring, −7 is a prime element. However, even among mathematicians, the term "prime number" generally means a positive prime integer.

Related Topics:
Ring theory - Abstract algebra - Ring

~ ~ ~ ~ ~ ~ ~ ~ ~ ~