We still haven't proven whether the number of primes below any given number always follows the same smooth approximation as its size grows infinitely large.
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Global / Unspecified, Global
WS01293
The Prime Number Theorem offers an excellent approximation, but the finer details of exactly how actual prime counts deviate from this smooth prediction remain tied to the still-unproven Riemann Hypothesis. Fully resolving this would refine one of number theory's most central results.