“ Nature and the universe is all about continuous quantities; integral quantities and whole numbers represent an abstraction. ”
Hard disagree. This is the problem with math disconnected from physics. The real world is composed of quanta and spectra, i.e. reality is NOT continuous!
Certainly Turing and Godel showed that computation is not universal (complete). Looking at one element of number theory in isolation seems unproductive? Arithmetic space is staggeringly complex, but structured, layered. IMHO number theory is like a hall of mirrors without a defined interface with physics. See Yang Mills mass gap.