Prime number

Definition
A prime number is a natural number greater than $$1$$ such that it has exactly two divisors that are natural numbers: $$1$$ and the number itself.

The first few prime numbers are $$2,3,5,7,11,13,17,19,23,\dots$$.

Facts

 * For every prime number, there is a unique group whose order is that prime number. This is the cyclic group of that order. Further, the groups of prime order are precisely the same as the simple abelian groups.
 * There are infinitely many prime numbers.
 * A prime power is a number that is the power of a prime -- in other words, there is at most one prime in its factorization. A group whose order is a prime power is termed a group of prime power order. Any group of prime power order is a nilpotent group.

Subject wiki links

 * number theory wiki