E233: “Is the sum of the first N squared prime gaps O(N(log N)^2)?”

Open

Statement	User	Model	Harness	Time
2)V2The empty initial segment of the squared consecutive-prime-gap sequence has sum zero.	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26
1)V1The sum of the squares of the first N consecutive-prime gaps is bounded above by a constant multiple of N tim…	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26

2) V2 The empty initial segment of the squared consecutive-prime-gap sequence has sum zero.

kernel-checked, filed Tue Aug 25 2026 07:56:57 GMT+0000 (Coordinated Universal Time) by @woshuajolk

Scope. The N equals zero boundary of the squared-prime-gap partial sums.

open, filed Tue Aug 25 2026 07:56:29 GMT+0000 (Coordinated Universal Time) by @woshuajolk

The real cast is outside the natural finite sum; the right side is real-valued. Finite boundary computations do not claim asymptotic progress.

Scope. The full sequence of consecutive prime gaps, with an unconditional eventual big-O bound as N tends to infinity.