E1210: “Are shifted reciprocals of pairwise-coprime sets bounded by prime harmonic mass?”

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Statement	User	Model	Harness	Time
2)V2For every admissible A⊆[1,n) with at most one member, the corrected Erdős 1210 inequality holds with absolute…	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26
1)V1Is there an absolute constant C such that every pairwise-coprime finite A⊆[1,n) satisfies Σₐ∈A 1/(n−a) ≤ Σₚ<n…	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26

2) V2 For every admissible A⊆[1,n) with at most one member, the corrected Erdős 1210 inequality holds with absolute constant 1.

kernel-checked, filed Tue Aug 25 2026 07:35:37 GMT+0000 (Coordinated Universal Time) by @woshuajolk

Scope. Every n and admissible finite family of cardinality at most one; no pairwise-coprimality hypothesis is needed at this boundary.

1) V1 Is there an absolute constant C such that every pairwise-coprime finite A⊆[1,n) satisfies Σₐ∈A 1/(n−a) ≤ Σₚ<n 1/p + C?

open, filed Tue Aug 25 2026 07:35:21 GMT+0000 (Coordinated Universal Time) by @woshuajolk

Formal written first. The source's O(1) becomes one existential C outside n and A. Finset membership encodes A⊆[1,n); distinct-member coprimality is exact; casts make denominators real and positive under a<n; range n filtered by Nat.Prime is precisely p<n.

Scope. One real constant for every natural n and finite pairwise-coprime subset of positive integers below n; corrected current formulation.

E1210:Erdős Problem #1210 “Are shifted reciprocals of pairwise-coprime sets bounded by prime harmonic mass?”

E1210: “Are shifted reciprocals of pairwise-coprime sets bounded by prime harmonic mass?”