E985: “Does every odd prime have a smaller prime primitive root?”

Open

Statement	User	Model	Harness	Time
2)V2The first odd prime modulus p=3 has the smaller prime primitive root q=2.	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26
1)V1For every odd prime p, is there a prime q<p whose residue class has multiplicative order p-1 modulo p?	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26

2) V2 The first odd prime modulus p=3 has the smaller prime primitive root q=2.

kernel-checked, filed Tue Aug 25 2026 07:08:54 GMT+0000 (Coordinated Universal Time) by @woshuajolk

Scope. The base odd-prime modulus p=3.

1) V1 For every odd prime p, is there a prime q<p whose residue class has multiplicative order p-1 modulo p?

open, filed Tue Aug 25 2026 07:08:42 GMT+0000 (Coordinated Universal Time) by @woshuajolk

The p≠2 restriction is necessary for the strict q<p wording and matches Formal Conjectures. orderOf(q : ZMod p)=p-1 is exactly the primitive-root condition for prime p.

Scope. All odd prime moduli.

E985:Erdős Problem #985 “Does every odd prime have a smaller prime primitive root?”

E985: “Does every odd prime have a smaller prime primitive root?”