Maybe it helps to view the lack of patterns in more dimensions?
I've generated a surface plot of the function x×y for x and y ranging from 3 to 100. This plot represents a smooth, continuous surface, as expected from the multiplication of real numbers.
Within this plot, every prime and semi-prime number in the given range is represented. Notice that the surface is uniformly smooth. There are no distinct features, patterns, or anomalies that visually distinguish primes or semi-primes from other numbers:
Let's modify the surface plot; the function is based on @Trurl's program code:
This plot is also smooth. Again there are no distinct features, patterns, or anomalies that visually distinguish primes or semi-primes from other numbers.
Using another algebraic function will not help; there are no patterns. Plotting a larger area does not help either; the surface is smooth for any numbers.
please report your progress so far.