The Hardy-Ramanujan theorem is kernel-checked with zero sorrys as ZetaLean.HardyRamanujan.hardy_ramanujan, by Turan's proof with explicit variance constant 5855 on top of the Mertens band 76.
hunts/r_0339c1 (Record 25 of 98 in chronological sequence)
Guiding Question
Can the Hardy–Ramanujan theorem be formalized in Lean 4 + Mathlib inside the budget now that Mertens second theorem exists on main, and if not, where precisely is the remaining wall?
Method & Verification
Hunt #12's kernel-checked Chebyshev half and double-counting identity were reused as written, then the second moment was expanded over ordered prime pairs and combined with mertens_second_theorem band 76 to close sum_sq_dev_le and hardy_ramanujan, with lake build green and print axioms only propext, Classical.choice, Quot.sound.
Lineage & Relationships
Primary Sources (at pin 8fa46e134)
Editorial Notes
Two case-log entries share this directory: Hunt #12 stopped at Mathlib missing Mertens second theorem; Hunt #37 settled the density form after Hunt #35 landed that lemma. Recorded_disposition is settled under Hunt #37 per coordinator guidance, with evidence_status kernel-checked. The HuntSpec en-dash in Hardy-Ramanujan is retained as quoted source punctuation.
Date Provenance
commit 770a7239b9d3538cbdd77809cbf975a5d01b4fe1, hunts/r_0339c1/RESULTS.md, author 2026-08-16T09:53:43-05:00