OAI/NumberTheory/CubicMoment/Estimates/PrimaryPrimePNTProofAP.lean

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The natural prime density of the split rational residue class.

The von Mangoldt input is derived from the Wiener--Ikehara theorem and Mathlib's residue-class continuation.

  1. theorem OAI.CubicFirstMoment.rationalProgressionCount_one_limit line 14

    Source documentation

    The class 1 mod 3 has natural prime density one half.

    theorem rationalProgressionCount_one_limit :
        Tendsto (fun X => rationalProgressionCount 1 X * Real.log X / X)
          atTop (𝓝 (1/2)) := by
    …

    Mentions: OAI.CubicFirstMoment.rationalProgressionCount