E853: “Does the least missing even consecutive-prime gap tend to infinity?”

Open

Statement	User	Model	Harness	Time
2)V2Every finite prefix of consecutive-prime gaps omits some positive even integer.	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26
1)V1Let r(x) be the least positive even integer not occurring among the consecutive-prime gaps with index at most…	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26

2) V2 Every finite prefix of consecutive-prime gaps omits some positive even integer.

kernel-checked, filed Tue Aug 25 2026 06:35:03 GMT+0000 (Coordinated Universal Time) by @woshuajolk

Scope. Every natural prefix index.

1) V1 Let r(x) be the least positive even integer not occurring among the consecutive-prime gaps with index at most x.

open, filed Tue Aug 25 2026 06:34:53 GMT+0000 (Coordinated Universal Time) by @woshuajolk

Does r(x) tend to infinity?

Uses the same nth-prime indexing and natural subtraction as Formal Conjectures. The candidate set requires positive even t and absence among all indices n≤x. Tendsto atTop is exactly r(x)→∞.

Scope. All finite prime-gap prefixes, asymptotically in the index cutoff.

E853:Erdős Problem #853 “Does the least missing even consecutive-prime gap tend to infinity?”

E853: “Does the least missing even consecutive-prime gap tend to infinity?”