Now that I think about, theres an easy way of disproving the primality of the number 2 within the domain of maths itself.
The numbers 1-9 are artifacts of our mod9 numeric system. However there are other modular systems possible and they are used frequently. For example measuring seconds is done with a mod59 system. If you use a mod1 system, you follow the number 1 with 10 so the number line progresses like this: 1,10,11,100,101,110.111,1000...
This makes proving that 1+1 does not nessesarily equate to 2 a cinch as under this equally valid numeric system 1+1=10.
As a an interesting cultural synchronocity of this, the Hopi clan of native americans do not group entities together like western people, they treat all percieved objects as distinct from one another. For example a western person would say that there are two trees on the hill wheras a hopi would say that there is a tree on the summit if the hill and a tree on the edge of the slope. Interestingly this cognitive distinction is instilled in their very language. Since the hopi's (and many other native american tribes's) language is
polysynthetic, they can encode a single word with great detail in form and spacial oriontation. Xei will probably recall me going on about this in the overpopulation thread.