A number is prime if its only divisors are 1 and itself. A definition we are all familiar with. A fact we could teach a child once we think they are old enough to understand.

Given the definition, 2 is a prime number. Out of the infinite number of primes, 2 is the only one that is even.

But 2 never had a chance of not being prime. Contrast this with 3. We travel along the number line 1, 2, 3. We know that 1 and 3 are going to be divisors of 3 (as every number can be divided by itself and 1). There is a number – 2 – of which we can ask the question: is this a divisor of 3? The answer of course is ‘No’ so 3 is prime. But we got to ask the question. 3 had a chance not to be prime before we asked the question.

When you get to 4, you know that 1 and 4 are going to be divisors of 4. There are two candidates – 2 and 3 – and we ask if they are divisors of 4. Of course, 2 is a divisor and 3 is not a divisor. 4 is therefore not prime. It is the first composite number.

Going along the sequence of counting numbers there are always candidates for being divisors, but this never applied to 2: there is no whole number in there between 1 and 2 which 2 could have been divided by.

Don’t get me wrong: I am not of the opinion that 2 should not be a prime number. The prime numbers are the so called “building blocks” for all of the numbers: they allow us to construct all numbers from prime numbers in terms of multiplication. Without 2 being prime this would not be possible, and the “fundamental theorem of arithmetic” would fall apart. It is just that 2’s solitary evenness amongst a sea of odd primes feels untidily pattern-breaking. We say that all prime numbers are odd … apart from 2. We have to make an exception for 2. We have to explain that it is the only even prime number. That need to explain feels like a small imperfection in the abstract world of numbers, a world that stands in contrast to the eternally imperfect physical world we must inhabit every day.