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An integer greater than one is called a
prime number if
its only positive divisors (factors) are one and itself.
For example, the prime
divisors of 10 are 2 and 5, and the first six
primes are 2, 3, 5, 7, 11, and 13.
By the fundamental theorem of arithmetic we know that all
positive integers factor
uniquely into a product of primes.
Technical comment on the definition:
In the integers we can easily prove the following
 A positive integer
p, not one, is prime if whenever it divides the product of integers
ab, then it divides a or b (perhaps both).
 A positive
integer p, not one, is prime if it can not be decomposed into factors
p=ab, neither of which is 1 or 1.
When we study other number systems, these properties may not hold.
So in these systems of integers (often called rings) we often make the
following definitions:  Any element which divides one is a
unit.
 An element p, not a unit, is prime if
whenever it divides the product of integers ab, then it divides
a or b (perhaps both).
 An element p, nonzero
and not a unit, is called irreducible if it can not be
decomposed into factors p=ab, neither of which is a
unit.
See Also: PrimeNumberThm, PrimeGaps Related pages (outside of this work)
