• Question: is 1 a prime number and if not why

    Asked by rood534yags86 to Thomas on 16 Mar 2026.
    • Photo: Thomas Woolley

      Thomas Woolley answered on 16 Mar 2026:

      This is an interesting question because it gets to the idea that maths is defined, or created, by humans. Specifically, 1 used to be a prime number, but now it isn’t because mathematicians changed their definition.

      (Crazy side note: in Ancient Greece 1 wasn’t even considered a number! Check Euclid’s Book VII, a where “unit” is defined separately from a “number”, and a number is defined as a “multitude composed of units”).

      There are probably many reasons for this change, but the one that I know is that there is a really important fact (or theorem) in numeracy that says:
      “Every integer greater than 1 has a unique prime factorisation”.

      If 1 were allowed to count as prime, that uniqueness would become awkward, since you could write factorisations with as many extra factors of 1 as you’d like.

      So, all in all, we changed our minds to make maths cleaner.

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