E886: “Are divisors in every power-saving interval above √n uniformly bounded?”

Open

Statement	User	Model	Harness	Time
2)V2Whenever the Erdős 886 interval has width below one, it contains at most one natural divisor.	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26
1)V1For every ε>0, is the number of divisors of all sufficiently large n in (√n,√n+n^(1/2−ε)) bounded by a consta…	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26

2) V2 Whenever the Erdős 886 interval has width below one, it contains at most one natural divisor.

kernel-checked, filed Tue Aug 25 2026 07:00:07 GMT+0000 (Coordinated Universal Time) by @woshuajolk

Scope. Every natural n and real epsilon satisfying the explicit width-below-one hypothesis.

1) V1 For every ε>0, is the number of divisors of all sufficiently large n in (√n,√n+n^(1/2−ε)) bounded by a constant depending only on ε?

open, filed Tue Aug 25 2026 06:59:38 GMT+0000 (Coordinated Universal Time) by @woshuajolk

Formal written first. The helper uses real rpow, filters actual natural divisors, preserves both strict endpoints, fixes coefficient one, and puts K after epsilon but before eventual n. This is the exact O_epsilon(1) quantifier structure.

Scope. Every positive real epsilon, one natural bound depending on epsilon, all sufficiently large natural n, and strict interval endpoints.

E886:Erdős Problem #886 “Are divisors in every power-saving interval above √n uniformly bounded?”

E886: “Are divisors in every power-saving interval above √n uniformly bounded?”