Stop saying that 2 is the only even prime

One of my biggest pet peeves is the phrase “2 is the only even prime”. This phrase appears repeatedly in various sources that list number facts, including:

• The Penguin Dictionary of Curious and Interesting Numbers by David Wells, which states: “2 is the first prime and the only even prime.”
• Archimedes Lab in a list on number facts places “2 is the only even prime” first amongst its descriptions of 2.
• A Math StackExchange post by Rhys Hughes, listing it as the only fact about 2.
• In a list on GitHub pages, Erich Friedman (retired mathematics professor at Stetson University) has “2 is the only even prime” as the only fact about 2.
• The Wikipedia page for the number 2, which opens by noting: “It is the smallest and the only even prime number.”
• A Best Life article listing it as fact #2.
• Science Sparks, stating: “2 is the only even prime number!”
• Damtindia.com infographic series.
• Finally, in a slightly less egregious example, Constance Reid in her book From Zero to Infinity (yet another book about facts about each numbers) wrote about the number 2. After describing the number for a few pages, she finally gets to the observation that “With the exception of two, they [primes] are odd, since all even numbers after two are divisible by the prime two and hence composite.”

In addition to these examples I found I can anecdotally attest that I have heard this “fact” all the way from primary school, where I remember being taught it at age 10, to even university mathematics classes where I still heard it uttered as if it was something worth noting.

You don’t have to worry - I am not about to argue that it isn’t true. Of course, 2 is the only even number that is prime. Something that continues to depress me is that when I make objection to this phrase in conversation, people nearly always reply “But 2 is the only even prime!”

My actual issue with this phrase is that I find it so in-utterably uninteresting that it extends beyond even tautologies. The word “even”, lest we forget, refers to numbers that are divisible by 2. The word “prime” refers to numbers that are only divisible by 1 and themselves. The phrase “2 is the only even prime” can be rewritten - “2 is the only number that is only divisible by 1 and itself, which is also divisible by 2” or perhaps “2 is the only number that is only divisible by 1 and 2.” Even the phrase “2 is the only prime divisible by 2” seems a dull one.

What makes this phrase so irksome is not just that it is tautologically and trivially obvious, but that it requires obscuring the truth in order to work. If we had common terms for numbers divisible by 3 or 5—say “threeven” and “quinquesectable”—then similar trivial statements would arise:

• “3 is the only threeven prime.”
• “5 is the only quinquesectable prime.”
• “17 is the only seventeenable prime.”

It isn’t hard to imagine a world in which there were a word for numbers divisible by 5. After all, our number system is base 10, and as such it is very easy to tell which numbers are divisble by 2 or 5 as they are the prime factors of 10. For numbers divisible by 2 (even numbers) we can simply check the last digit: 0, 2, 4, 6, 8 all mean it is even, anything else means it’s odd. For numbers divisible by 5 (our new quinquesectable numbers) we can simply check the last digit: 0, 5 both mean it is quinquesectable, anything else means it isn’t.

In fact we could extend this to all the primes and create an infinite series of “facts”. 2 is the only prime divisible by 2, 3 is the only prime divisible by 3, 5 is the only prime divisible by 5, 17 is the only prime divisible by 17. In other words, these are all primes.

This kind of statement reflects a shallow understanding of prime numbers. Primes aren’t just an isolated property some numbers happen to have—they are the foundational building blocks of all integers. Every single integer has a prime factorisation:

• 2 -> 2
• 3 -> 3
• 4 -> 2²
• 5 -> 5
• 6 -> 2*3
• 7 -> 7
• 8 -> 2³
• 9 -> 3²
• 10 -> 2*5

Not only does every integer above 1 have a prime factorisation, but they all have only one unique prime factorisation. This allows for a perspective of integers where each prime can be considered like the elements of chemistry - the most basic unit that the others are made out of, and each composite number can be considered like the compounds of chemistry - combinations of those basic units. If we were already predisposed to thinking about numbers in these terms (perhaps in a world where we wrote numbers down using the factorisation), then the observation would be stupefying. “2 is the only number containing just one 2 in its factorisation”

Part of the persistence of this fact may stem from the cultural emphasis on evenness and symmetry. The number 2 holds special weight in language, logic, and daily life—think of binary systems, dichotomies, partnerships. Because of this cultural prominence, we end up with a set of “interesting” properties. Some numbers are even. Some numbers are prime. But only one number is both, how interesting! Not.