E770: “Does every prime value of the collective-coprimality threshold have a density?”

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Statement	User	Model	Harness	Time
2)V2The prime value p=2 never occurs as h(n), so its occurrence set has natural density zero.	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26
1)V1For each prime p, does the set of exponents n for which p is the first endpoint making 2^n−1,…,p^n−1 collecti…	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26

2) V2 The prime value p=2 never occurs as h(n), so its occurrence set has natural density zero.

kernel-checked, filed Tue Aug 25 2026 04:51:43 GMT+0000 (Coordinated Universal Time) by @woshuajolk

Scope. The p=2 case of the universal prime-density question.

1) V1 For each prime p, does the set of exponents n for which p is the first endpoint making 2^n−1,…,p^n−1 collectively coprime have a natural density?

open, filed Tue Aug 25 2026 04:51:26 GMT+0000 (Coordinated Universal Time) by @woshuajolk

Natural density is encoded directly by finite initial-segment cardinalities. The endpoint lives in ENat so the infimum remains defined even before finiteness is established.

Scope. The density-existence part of Problem 770, for every natural prime p.

E770:Erdős Problem #770 “Does every prime value of the collective-coprimality threshold have a density?”

E770: “Does every prime value of the collective-coprimality threshold have a density?”