Truth of Fundamental Theorem of Arithmetic beyond some large number Let $n$ be a ridiculously large number, e.g., $$\displaystyle23^{23^{23^{23^{23^{23^{23^{23^{23^{23^{23^{23^{23}}}}}}}}}}}}+5$$ which cannot be explicitly written down provided the size of the universe. Can a Prime factorization of $n$ still be possible? Does it enter the realms of philosophy or is it still a tangible mathematical concept?

Yes, there exists a unique prime factorization.
No, we probably won't ever know what it is.
