“So far” with respect to some particular problem you’re solving or process you’re following. If you’re talking about all problems, you’d have to do some research. Perhaps OEIS [1] could help you. Or you could interview some number theorists to find out who is working in large numbers and ask them.
Asking the question in general, though, is equivalent to asking “what is the largest number anyone has thought of?” I would have to interrogate your motives to know why you would want to ask such a question.
Intuitionists would scoff at the idea of a “number larger than anyone could describe.” That’s heading into the territory of the interesting number paradox [2]. Intuitionism avoids this paradox by stating that numbers (and sets of numbers) have no existence independent of their construction.
" “what is the largest number anyone has thought of?” I would have to interrogate your motives to know why you would want to ask such a question..."
I ask because it's absurd. A particular large number is a logical thing regardless of whether a person thought of it before or whether it describes a distinct natural phenomenon. This follows from the set theory axioms, as well as Real numbers and infinitely many other number systems. To restrict our capacity to think of numbers to only numbers that people can enumerate or numbers that describe natural phenomena seems arbitrary and onerous. We construct the Real number simply by considering the limits of convergent sequences to be numbers. I don't see anything transgressive about this idea. Sure, some numbers are not computable, and other numbers can't be represented with marbles; they still have utility and there is no reason to make the concept of "numbers" exclusive.
Asking the question in general, though, is equivalent to asking “what is the largest number anyone has thought of?” I would have to interrogate your motives to know why you would want to ask such a question.
Intuitionists would scoff at the idea of a “number larger than anyone could describe.” That’s heading into the territory of the interesting number paradox [2]. Intuitionism avoids this paradox by stating that numbers (and sets of numbers) have no existence independent of their construction.
[1] https://oeis.org/
[2] https://en.wikipedia.org/wiki/Interesting_number_paradox