Serializing an n-dimensional space?

I showed with a python program by exhaustion that:

Is unique for x, y, z an ordered triple of integers from {0..10}.
In decimals:

The closest any two values of this function over these triples is:
0.00041135335253
Which is nice because it means you could round every value to the nearest 10,000th and still have uniqueness.
I find it hard to try and figure out whether one can always map this way an ordered n-tuple {X1, X2,...Xn}
as an non-surjective injection to rational numbers with the formula {X1/P[1]+ X2/P[2]+ X3/P[N}} where P[1], ... P[N] are the N smallest primes larger than N, but I'll suggest it as a conjecture.