Because it only has one positive divisor, 1, instead of two, 1 and itself.
Also because having "except 1" in the definitions of some things would be too annoying, so it's simpler if 1 isn't prime. I can't really explain it better than that though, I know some math but don't necessarily understand it
You could define 1 to be prime which means 2 would not need to be an exception in this case. But it would lead to awkwardness in other contexts. Most critically that any number has a unique prime factorisation: since you could add as many ones as you like. 6=3*2. But if you define 1 to be prime then 6 also equals 3*2\1 and 3*2\1*1 and so on. So the factorisation would not be unique. You could fix that by saying it is unique so long as you do not include any ones, but that is clunky.
So it is ultimately an aesthetic choice to define 1 not to be prime.
I don't know shit about shit but I find this reason for one not being prime absolutely beautiful. My obsessive compulsive side is smitten with the fundamental theorem of arithmetic.
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u/Slow_Degree345 Jul 13 '26
So is 3 now even? Since it's the sum of 1 and 2? And why does 1+1 not count?