What, if any, discussion or musing, has sprung from what I take as a logical similarity between prime numbers and the dimensions of any regular geometric space?
Consider:
Primes, by multiplication, span the space of numbers by allowing some plurality of primes to yield any non-prime. This is similar to how any point in N-space can be defined as a weighted combination of coordinates on any N axes defining that space.
By the same token, no prime is useful in describing any other prime, the same way that any point on an axis has no projection to any other axis defining any space defined by its own axis. Primes might be described as being orthogonal to each other, and primes 1 to N can be described as defining a "space" of non-primes, a subset of those non-primes greater than themselves.
My observation from the above is that primes map the number line in a manner similar to that by which axes map a Cartesian space. I do not have any more penetrating insights into the matter ready at hand, but I'd be delighted it anyone else found this initial observation in any way interesting.