Sure, whether you need to work to earn a living depends on the standard of living and risk level you're comfortable with. But I think it's possible to set a reasonable upper bound. Say, around the point where your interest income at a typical risk-free rate, after reinvestment to keep pace with inflation, would put you among the highest earners in the world if it were ordinary income. Defining "highest earners" as those in the top two US tax brackets, that amount is currently around $8-10M, or on the order of 2^23 present-day dollars.

Personally I think on the order of 2^22 dollars reasonably qualifies as well. Maybe that's because of the standard of living I'm used to. Certainly if you have 2^24 dollars and you don't think you're rich, you have a definition of wealth that ignores a major qualitative difference in what a person can afford to do. Above 2^23 dollars, I think additional wealth begins to put you more in the realm of the low-level aristocracy and rulers than the merely rich.