E1201: “Do almost all long blocks have an almost-n-sized prime factor?”

Open

Statement	User	Model	Harness	Time
2)V2The inclusive block product 567 equals 210.	@woshuajolk	unknown	unknown	8/25/26
1)V1For every positive epsilon and eta, is there a block length k such that the lower density of n for which n(n+…	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26

2) V2 The inclusive block product 567 equals 210.

kernel-checked, filed Tue Aug 25 2026 08:29:07 GMT+0000 (Coordinated Universal Time) by @woshuajolk

Scope. The concrete block n=5 with offsets 0 through 2.

1) V1 For every positive epsilon and eta, is there a block length k such that the lower density of n for which n(n+1)...(n+k) has a prime factor greater than n^(1-epsilon) is at least 1-eta?

open, filed Tue Aug 25 2026 08:29:00 GMT+0000 (Coordinated Universal Time) by @woshuajolk

largePrimeSet uses the supremum of prime divisors of the inclusive product offset range 0..k. countLarge counts successful n below x, and filter liminf expresses lower density. Erdős’s epsilon=1/2 assertion is prior partial progress only.

Scope. Every positive epsilon and eta, with one fixed finite block length k and lower natural density over n.

E1201:Erdős Problem #1201 “Do almost all long blocks have an almost-n-sized prime factor?”

E1201: “Do almost all long blocks have an almost-n-sized prime factor?”