Admitting 1 as a prime number messes up all these theorems which otherwise have simple statements If the messing up accomplished something of real value it would be all right By this I mean that if the explanations had to be complicated in order to help people understand some subtle point that was of real interest that would be all right But in these examples and many others the additional complication introduced by admitting 1 as a prime number does not lead anyone to any better understanding of what is going on