In the below picture I have charted the distribution of numbers below n by factor count. The bottom line is for all numbers under 100,000 then 200,000 ... all the way to 1,000,000.
They seem to tend to a specific set of numbers. Right now I am limited with my data set and was hoping someone could enlighten me as to if this goes on to infinity or does it tend to a specific number set?
The numbers in the chart below were calculated by:
Primes under 100,000 - 9,592 - I then split up how many had two factors and three and so on and divided those numbers by 9,592 and that produced the bottom line in the chart below.
The first number is always one because I divide the number of primes under n by that same number. Then the line rises because there are more composite numbers with two factors than there are prime numbers. It rises again with three and then starts to fall as the count of composites with 4 factors starts to trend in the other direction.
The reason I am doing this is for recreation prime research and with the thought that if we can see how the distribution of prime factors works with large numbers maybe this could develop a reasonable prime counting calculation.