Nowadays, the number one is not considered a prime, but this was not always the case.  After all, if we take the definition of a prime number to be a number whose only divisors are one and itself, the number one seems to satisfy that. 

However, when considering the fundamental theorem of arithmetic, which states that every positive whole number, or positive integer, can be written as a unique product (multiplication) of primes, if one is also considered a prime, then it would give multiple ways of expressing a number as a product of primes. For example, 14 = 2 x 7 = 1 x 2 x 7 = 1 x 1 x 2 x 7 and so on. 

So, it was decided that one should not be considered prime.  The definition of a prime can be slightly modified to state that a prime number is a positive integer which has exactly two distinct factors, one and itself.  Using this definition, one is definitely excluded from the set of primes.

In fact, the number one is considered neither prime nor composite, since it cannot be written as a product of primes.  The reciprocal of an integer x is 1/x.  The number one is the only positive integer which has an integer reciprocal.  For this reason, it is called a unit.