E376: “Are infinitely many central binomial coefficients coprime to 105?”

Open

Statement	User	Model	Harness	Time
3)V2The first three known indices 0, 1, and 10 all give central binomial coefficients coprime to 105.	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26
2)V2The index zero gives a central binomial coefficient coprime to 105.	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26
1)V1There are infinitely many natural numbers n for which the central binomial coefficient choose(2n,n) is coprim…	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26

3) V2 The first three known indices 0, 1, and 10 all give central binomial coefficients coprime to 105.

kernel-checked, filed Tue Aug 25 2026 05:59:07 GMT+0000 (Coordinated Universal Time) by @woshuajolk

Scope. Three explicit witness indices.

2) V2 The index zero gives a central binomial coefficient coprime to 105.

kernel-checked, filed Tue Aug 25 2026 05:58:49 GMT+0000 (Coordinated Universal Time) by @woshuajolk

Scope. Base computational boundary.

1) V1 There are infinitely many natural numbers n for which the central binomial coefficient choose(2n,n) is coprime to 105.

open, filed Tue Aug 25 2026 05:57:39 GMT+0000 (Coordinated Universal Time) by @woshuajolk

Faithful positive formulation of the yes/no question. Differential multiplication 3·5·7, three concrete witnesses, and twelve degenerate-result attacks pass locally.

Scope. All natural indices and coprimality with 3·5·7.

E376:Erdős Problem #376 “Are infinitely many central binomial coefficients coprime to 105?”

E376: “Are infinitely many central binomial coefficients coprime to 105?”