Alan Turing showed that it is almost impossible to differentiate between computer programs that run for a long time before halting with an answer and those programs that run forever without halting and achieving an answer.
Long-running “busy beaver” programs are
the subject of a Quanta article that has important information about the
limitations of mathematics as a whole.
See https://www.quantamagazine.org/the-busy-beaver-game-illuminates-the-fundamental-limits-of-math-20201210/
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