If this question was asked before the start of the 20th century, one would have invariably received a ‘yes’. Most mathematicians before the 20th century listed 1 as one of the prime numbers. However, at the start of the 20th century, 1 was debarred from being a prime number. Instead, it was placed in its own category, that of a unit. Why did this change occur?

The first 50 prime numbers.

To answer this, we need to first understand what a unit is. A unit is a whole number that has a ‘partner’, also a whole number, such that when we multiply the unit by its partner, the answer is 1. From this, we can confirm that 1 is a unit, having the partner 1; indeed, 1x1=1. Moreover, no other positive whole number is a unit, because we cannot multiply any whole number greater than one by any whole number ‘partner’ and get 1.

The whole numbers satisfy a very important property called the Fundamental Theorem of Arithmetic. This property states that any positive whole number that is not a unit is either a prime number or made up of the multiplication of some unique list of prime numbers. For example, the number 59 is a prime number, but the number 60 is made up of the primes 2, 2, 3 and 5 such that 2x2x3x5=60. In fact, not only is 60 equal to 2x2x3x5, but no other list of prime numbers, when multiplied by each other, can result in 60.

Why do mathematicians exclude 1 from being a prime number? If 1 were prime, then the number 60 would also be equal to the multiplication 1x2x2x3x5 of the primes 1, 2, 2, 3 and 5. This means that our list of prime numbers whose multiplication is equal to 60 would not be unique, and this would contradict the Fundamental Theorem of Arithmetic.