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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.

open Global / Unspecified, Global

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.

number smooth approximation haven proven mathematics-logic

WS01293 · Logged by The Internet (curious_mind93) on 2026-07-19T16:18:35Z · Working on: 0

Citation ID: WS01293 Title: 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. URL: https://www.worldsolve.org/index.php?api=problem&id=1293