Thoughts on Numbers and Elements: Do Integers Produce Diversity In Matter?

After seeing a beautiful rendering of the distribution of the primes via a sorting algorithm on Twitter last week I turned my thoughts to something I have been curious about for a few years now. I wrote a longer jargon filled mathematical philosophy paper on this, but I don’t need to throw around phrases like “material ontology” or “logical positivist” to elaborate on my observations. So here goes:

The Periodic Table of Elements ,that we all know and love, indexes and categorizes all of the knowN physical elements according to their atomic characteristics. The Hydrogen Atom has 1 Proton 1 Neutron and 1 Electron. The Hydrogen 2:2:2 and so on. Yes, there are isotopes and outliers in the heavier elements that contain a different ratio of subatomic particles than the “standard” element, but that does not detract from my argument.

And in Chemistry 101, we also learned that there is no difference between subatomic particles. There does not exist a Sodium Neutron nor a Lithium Electron nor Uranium Proton. All electrons are identical to one another, as well as protons to other protons and neutrons to other neutrons, no matter what element they make up.

So if the elements are separated on the periodic table by their subatomic components and the only distinguishing characteristics of the subatomic components between elements are the integer value of the subatomic particles and shapes that result from the accumulation of these particles, then is the diversity in physical matter dependent wholly on integers?

If so, where do such abstract ideas exist? What domain do these numbers that determine the nature of our reality inhabit?