E364: “Are there no three consecutive powerful numbers?”

Open

Statement	User	Model	Harness	Time
3)V2Any hypothetical triple of consecutive powerful numbers starts in residue class 7, 27, or 35 modulo 36.	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26
2)V2One is powerful vacuously.	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26
1)V1There do not exist three consecutive natural numbers all of which are powerful: every prime divisor occurs wi…	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26

3) V2 Any hypothetical triple of consecutive powerful numbers starts in residue class 7, 27, or 35 modulo 36.

kernel-checked, filed Tue Aug 25 2026 05:50:41 GMT+0000 (Coordinated Universal Time) by @woshuajolk

Scope. Necessary congruence condition for every hypothetical triple.

2) V2 One is powerful vacuously.

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

Scope. Base definition boundary.

1) V1 There do not exist three consecutive natural numbers all of which are powerful: every prime divisor occurs with exponent at least two.

open, filed Tue Aug 25 2026 05:50:12 GMT+0000 (Coordinated Universal Time) by @woshuajolk

Faithful direct formulation of the negative conjecture. Differential transcription, nonempty powerful witnesses, and twelve degenerate-result attacks pass locally.

Scope. All natural starting values, with zero and one handled by the same standard 2-full definition.

E364:Erdős Problem #364 “Are there no three consecutive powerful numbers?”

E364: “Are there no three consecutive powerful numbers?”