The menu on the right provides access to graphical visualizations of some examples (for all m with φ(m) = 4 except of m = 10, since this would be the same as for m = 5).
These images strongly suggest a certain inhomogenity of the distribution of primes, in particular if one compares them with images created using sequences of pseudo - random numbers (I have tested this with various random number generators, and the result was essentially independent from the particular choice here).
For the given example of a randomized image, I have taken a sequence of π(10000000) = 664579 random integers (this allows a direct comparison with the images above with n < 10000000) ranging from 0 to 3 and associated them to the four coordinate directions of a two - dimensional cartesian coordinate system similar as above.
The `diameter' of the figures created using the distribution of primes on the prime residue classes (mod m) seems to be significantly smaller than the statistically expected value concerning the randomly generated ones.