E145: “Do all moments of consecutive squarefree gaps have limiting means?”

Open

Statement	User	Model	Harness	Time
2)V2The enumerated squarefree-number sequence is strictly increasing and all consecutive natural gaps are positiv…	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26
1)V1For every nonnegative real exponent, the normalized moment sum of gaps between consecutive squarefree numbers…	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26

2) V2 The enumerated squarefree-number sequence is strictly increasing and all consecutive natural gaps are positive.

kernel-checked, filed Tue Aug 25 2026 04:24:08 GMT+0000 (Coordinated Universal Time) by @woshuajolk

Scope. The complete Nat.nth enumeration of natural squarefree numbers.

1) V1 For every nonnegative real exponent, the normalized moment sum of gaps between consecutive squarefree numbers converges as the cutoff tends to infinity.

open, filed Tue Aug 25 2026 04:22:38 GMT+0000 (Coordinated Universal Time) by @woshuajolk

The missing Formal Conjectures utility lemma that squarefree naturals are infinite is proved inline from infinitude of primes. Local build, positive-gap witnesses, independent real-subtraction transcription, prior-art review, and anti-restatement control all passed.

Scope. All real exponents α ≥ 0 for the complete increasing sequence of natural squarefree numbers.

E145:Erdős Problem #145 “Do all moments of consecutive squarefree gaps have limiting means?”

E145: “Do all moments of consecutive squarefree gaps have limiting means?”