  By defining the dimension of natural numbers as the number of prime factors,
all natural numbers smaller than 2^(n+1) (n is a natural number) can be
classified by their dimensions, and the count of numbers of each dimension
gives a dimensions distribution directly related to the distribution of prime
numbers. A triangle similar to Pascals triangle from some aspects can be
obtained by the ensemble of dimensions distributions. Some superficial
explorations have been done to this interesting triangle.
