Is there anything out there that talks about how primes are one dimensional numbers and composites can only be in dimensions greater than 1?
What I mean is, 4 would be a two dimensional number (2x2) same with 6 (2x3). 27 would be three dimensional (3x3x3) and so on. While primes can only be made up of themselves therefore they are one dimension.
Assuming you meant that 27 would be "three dimensional" but 9 would be "two dimensional", then the "dimension" of a number $n$ is the total number of prime factors, denoted $\Omega(n)$ (often read "big omega"). It is not usually called the dimension of a number, but if you really like to think geometrically, you can think about it as the greatest dimension in which the number is the "hypervolume" of a hyperrectangle with side lengths greater than 1.
See the following links for some information.