Note that 1 not being a Prime is important in other mathematical definitions.

If you accept 1 as a Prime, to make the definition of Prime "simpler", you would need to add "except 1" as a "complication" to those other definitions.

So you'd make one definition simpler by making others more complex.

That's not a good investment.

(The Wiki page notes some of these. e.g. see "Primality of one")

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