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Since I think R(10^100) is about as high as a reasonable person would want to go, I'll only be adding other improvements if they are interesting enough. For example, the numbers involved are well over the limit that the gmpy2 documentation states as the start of its speed advantage over python ints, so it might be time for a gmpy2 or GMP port to compare with vanilla python. So for possibly the last time, please verify the value of R(10^120) with other implementations.