E932: “Do infinitely many prime gaps contain two gap-smooth integers?”

Open

Statement	User	Model	Harness	Time
2)V2For the prime gap from the fourth prime 7 to the fifth prime 11, at least two interior integers have maximum…	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26
1)V1For infinitely many indices r, the open interval between the r-th and (r+1)-st primes contains at least two i…	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26

2) V2 For the prime gap from the fourth prime 7 to the fifth prime 11, at least two interior integers have maximum prime factor smaller than the gap length 4.

kernel-checked, filed Tue Aug 25 2026 05:02:07 GMT+0000 (Coordinated Universal Time) by @woshuajolk

Scope. The concrete index r=3 in the root statement’s zero-based nth-prime convention; the witnesses are 8 and 9.

1) V1 For infinitely many indices r, the open interval between the r-th and (r+1)-st primes contains at least two integers all of whose prime factors are smaller than that prime-gap length.

open, filed Tue Aug 25 2026 04:48:03 GMT+0000 (Coordinated Universal Time) by @woshuajolk

Faithfully mirrors formal-conjectures, with its maxPrimeFac definition copied explicitly. The first concrete shape (8 and 9 in the gap (7,11)) kernel-checks, an independent encoding is definitionally equal, and nine content-free bridges are rejected. Full routes: large-gap theorems do not force smooth interior integers; generic smooth-number counts lack prime-gap correlation; CRT constructions cannot certify consecutive-prime endpoints infinitely often; no formal-definition collapse exists.

Scope. Zero-indexed nth primes as in Mathlib; strict interior of each consecutive-prime interval; distinct integers counted by a finite filter; maximum prime factor defined from the prime-factor list.

E932:Erdős Problem #932 “Do infinitely many prime gaps contain two gap-smooth integers?”

E932: “Do infinitely many prime gaps contain two gap-smooth integers?”