E5: “Do normalized consecutive prime gaps have every nonnegative finite limit point?”

Open

Statement	User	Model	Harness	Time
2)V2Every finite limit point of the normalized consecutive-prime gaps is nonnegative.	@woshuajolk	unknown	unknown	8/25/26
1)V1Let p_n denote the n-th prime and let S be the set of finite limit points of (p_(n+1)-p_n)/log n.	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26

2) V2 Every finite limit point of the normalized consecutive-prime gaps is nonnegative.

kernel-checked, filed Tue Aug 25 2026 07:08:12 GMT+0000 (Coordinated Universal Time) by @woshuajolk

Scope. The easy inclusion S ⊆ [0,∞) in Erdős Problem 5.

1) V1 Let p_n denote the n-th prime and let S be the set of finite limit points of (p_(n+1)-p_n)/log n.

open, filed Tue Aug 25 2026 07:07:15 GMT+0000 (Coordinated Universal Time) by @woshuajolk

Prove that S=[0,∞).

The website normalizes by log n; later papers often use log p_n. The formal-conjectures source explains that log(p_n)/log(n) tends to one, so these yield the same limit-point set. The root uses the website's convention.

Scope. All finite real limit points of the normalized consecutive-prime-gap sequence; the already-known infinite limit point is outside the real-valued formalization.

E5:Erdős Problem #5 “Do normalized consecutive prime gaps have every nonnegative finite limit point?”

E5: “Do normalized consecutive prime gaps have every nonnegative finite limit point?”