Definition
Prime Number
A natural number
is prime if its only positive divisors are and : Here,
means that for some natural number . Thus a prime has exactly two positive divisors; in particular, is not prime.
Example
Prime and non-prime numbers
The first primes are
.
is prime: its positive divisors are and . is not prime: , so it also has divisors and . is not prime: it has only one positive divisor.