At the moment my area of research is Mersenne Primes. I am currently looking into a specifically large exponent, $\ 2^{112401533}-1$, and I can’t help but wonder how I would calculate how many digits a number like that would have. Has anyone got any ideas on ways to estimate the number of digits in large exponents of two? (Or any other number - the results do not have to be exact, but more akin to a smart estimate on the number of digits).
2026-04-03 12:59:27.1775221167
The number of digits in an exponent of two
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