Non-primality of 1 is a design decision made by the mathematical community. A convention with which one can agree or disagree. But it is part of a general patt

Non-primality of 1 is a design decision made by the mathematical community. A convention with which one can agree or disagree. But it is part of a general pattern that certain objects are "too simple to be simple" [0]. Here "simple" should be thought of as atomic, indecompossible, without smaller parts. - prime numbers are simple wrt multiplication, 1 is too simple to be prime - the zero ring is too simple to be a field - the trivial group is too simple to be a simple group - the empty topological space is not connected - etc... It turns out that if one adheres to this convention, then theorem statements generally become shorter, and have fewer side conditions. [0]: https://ncatlab.org/nlab/show/too+simple+to+be+simple https://ncatlab.org/nlab/show/too+simple+to+be+simple