The point of the article is that we don't consider a unit in a number system to be prime, and in the integers/rationals/reals 1 is a unit. Why we don't conside

The point of the article is that we don't consider a unit in a number system to be prime, and in the integers/rationals/reals 1 is a unit. Why we don't consider units to be prime is more than just it "makes more math look nicer." As discussed in the article, once we explored different types of number system (the example given is an adjoin of the square root of negative 5 to the integers) we were able to classify numbers that no-one would ever 'intuit' as prime: the units. The defining characteristic of these non-primes is shared by '1' in the integers/rationals/reals so it is consistent to call 1 a non-prime as well.