E409: “Do all sigma-minus-one iterations reach a prime?”

Open

Statement	User	Model	Harness	Time
2)V2The nontrivial orbit starting at four is 4→6→11, reaching a prime in two steps.	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26
1)V1Starting from any n>1, does repeated iteration of n↦σ(n)-1 eventually reach a prime?	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26

2) V2 The nontrivial orbit starting at four is 4→6→11, reaching a prime in two steps.

kernel-checked, filed Tue Aug 25 2026 05:43:03 GMT+0000 (Coordinated Universal Time) by @woshuajolk

Scope. The explicit starting value four.

1) V1 Starting from any n>1, does repeated iteration of n↦σ(n)-1 eventually reach a prime?

open, filed Tue Aug 25 2026 05:42:50 GMT+0000 (Coordinated Universal Time) by @woshuajolk

The exact affirmative RHS of the source answer placeholder. Orbit 4→6→11 validates nontrivial iteration and primality conventions; an independent transcription agrees.

Scope. All natural starting values greater than one.

E409:Erdős Problem #409 “Do all sigma-minus-one iterations reach a prime?”

E409: “Do all sigma-minus-one iterations reach a prime?”