I think you are confusing or conflating the definitions of "odd" and "prime". I find I can't follow your reasoning at all, so let me give you my reasoning. Th

I think you are confusing or conflating the definitions of "odd" and "prime". I find I can't follow your reasoning at all, so let me give you my reasoning. The accepted definition of "odd" is that when you divide by 2 you have a remainder of 1. Thus 7 is odd, because when you divide by 2 you get an answer of 3 with a remainder of 1. Similarly 15 is odd, because you divide by 2 to get an answer of 7 with a remainder of 1. The accepted definition of "even" is that when you divide by 2 there is no remainder. Thus 18 is even because when you divide by 2 you get 9 and no remainder. Rephrasing that, if you multiply any integer by 2, the result is always an even number. So 9 times 2 is 18, hence 18 is even. 23 times 2 is 46, hence 46 is an even number. Then zero times 2 is zero, hence zero is an even number.