E463: “Do least-prime-factor windows contain increasingly deep composite numbers?”

Open

Statement	User	Model	Harness	Time
2)V2For every prescribed margin B, there are natural numbers n and composite m such that m lies above n+B but bel…	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26
1)V1There should be a natural-valued function f tending to infinity such that, for every sufficiently large n, so…	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26

2) V2 For every prescribed margin B, there are natural numbers n and composite m such that m lies above n+B but below n plus its own least prime factor.

kernel-checked, filed Tue Aug 25 2026 04:26:46 GMT+0000 (Coordinated Universal Time) by @woshuajolk

Scope. Arbitrarily large isolated margins at some base n; no eventual or uniform-in-n assertion.

1) V1 There should be a natural-valued function f tending to infinity such that, for every sufficiently large n, some composite m lies above n+f(n) but below n plus the least prime factor of m.

open, filed Tue Aug 25 2026 04:24:58 GMT+0000 (Coordinated Universal Time) by @woshuajolk

Canonical source and both differential bridges compile locally. Eleven degenerate declarations all red as restatements. The existential growth condition is inhabited by the identity function. A direct negation exposes the required eventual counterexample. The whole attack uses prime squares to kernel-check arbitrarily large isolated least-factor windows, but these intervals are sparse and do not cover every sufficiently large base point.

Scope. The affirmative current formulation for all sufficiently large natural n, with f : ℕ → ℕ tending to infinity and strict inequalities.

E463:Erdős Problem #463 “Do least-prime-factor windows contain increasingly deep composite numbers?”

E463: “Do least-prime-factor windows contain increasingly deep composite numbers?”