Why Isn't 1 a Prime Number

Credit: ValueWalk

A number divisible only by 1 and itself is considered a prime number. 1 seems to conform to the definition; it is divisible by 1 and itself and by no other number. But the definition of prime numbers excludes 1. Why?

Many people think it's because, in the case of 1, 1 and itself are the same number. But this is far from the truth.

The Fundamental Theorem Of Arithmetic

Credit: Bubbly Primes

Before we can see why 1 is not considered a prime, we must learn the most basic arithmetic theorem. The Fundamental Theorem Of Arithmetic states that any number greater than 1 can be represented as the product of one or more prime numbers in only one way.

Let's take a look at an example. Consider any number greater than 1. Let's say 8. According to the theorem, 8 can be represented as the product of one or more prime numbers. And the primes numbers are 2, 2, and 2. 2 * 2 * 2 = 8.

Now, if we consider 1 to be a prime number, there will be an infinite number of ways 8 could be represented; 2 * 2 * 2 * 1, 2 * 1 * 2 * 1 * 2, etc.

See Also

 

The Fundamental Theorem Of Arithmetic Proof