E1106: “Eventually more than n prime divisors among the first n partition numbers.”

Open

Statement	User	Model	Harness	Time
2)V2The set of distinct prime factors accumulated from partition numbers through n is contained in the correspond…	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26
1)V1Let p(i) be the partition number of i.	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26

2) V2 The set of distinct prime factors accumulated from partition numbers through n is contained in the corresponding set through n+1.

kernel-checked, filed Tue Aug 25 2026 06:08:44 GMT+0000 (Coordinated Universal Time) by @woshuajolk

Scope. All natural n.

open, filed Tue Aug 25 2026 06:06:31 GMT+0000 (Coordinated Universal Time) by @woshuajolk

Is the number of distinct prime factors of ∏_{1≤i≤n}p(i) greater than n for all sufficiently large n?

Uses the product p(i), not the apparent p(n) prose typo in formal-conjectures. Part (i) is known; this verifier poses only open part (ii).

Scope. Eventual asymptotic claim over natural n.