Prime number theorem

Layer 0 — Mathematicsin the number-theory subtree

π(x) ~ x/ln x as x→∞ (Hadamard, de la Vallée Poussin 1896). Equivalent to ζ(s) having no zeros on ℜs=1; the error term sharpens under RH to O(√x log x) but the leading asymptotic is unconditional.

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