Hey guys I made a spreadsheet in excel where I went by this logic;

33.33% of all numbers from 0 to infinity are divisible by 3.

13.33% of all numbers are divisible by 5 and not divisible by 3.

5.74152% of all numbers are divisible by 7 and not 3 and 5.

3.174% of all numbers are divisible by 9 and not 3(wrong), 5, and 7

I didn't need to include divisors of 9 at all because they always overlap with 3, but I wanted to see what would happen.

Has anyone done this before? My observations don't make sense? Is this a logical exercise?

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    $\begingroup$ Sure what you will be obtaining is the Euler product for $\zeta(s)$ and the inclusion-exclusion represented by the Möbius function $\mu(n)$ $\endgroup$ – reuns Apr 7 at 1:23
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    $\begingroup$ Oh my goodness... with all due respect you're several hundred years late on this. See the wonderful Prime numbers and the Riemann hypothesis, as just one of hundreds of books that have done this. cambridge.org/core/books/… $\endgroup$ – David G. Stork Apr 7 at 1:23
  • $\begingroup$ Thank you that will help me understand hopefully, no offense taken. I'm just glad it is logical. $\endgroup$ – PrimeQuestion Apr 7 at 1:28
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    $\begingroup$ @PrimeQuestion Unlike some of the commenters, I love seeing enthusiasts rediscover certain math revelations that may have been found hundreds of years ago. It really helps to motivate understanding material more deeply, and well, is just great for math's future too! $\endgroup$ – Don Thousand Apr 7 at 2:11
  • $\begingroup$ It is great when someone "rediscovers" a question, but discouraging in that they cannot find a very very very well established results and resort to asking an online site instead. An important skill is to be able to find results and resources on your own. $\endgroup$ – David G. Stork Apr 7 at 2:39

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