E1056: “Can arbitrarily many consecutive interval products all equal one modulo a prime?”

Open

Statement	User	Model	Harness	Time
5)V2The Erdős 1056 interval-product conjecture holds for k=9 and k=10, witnessed by a factorial-residue collision…	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26
4)V2The conjectured modular interval construction exists for each of k=7 and k=8.	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26
3)V2The conjectured modular interval construction exists for each of k=4, k=5, and k=6.	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26
2)V2The conjectured modular interval construction exists for k=2 and k=3.	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26
1)V1For every k at least two, some prime admits k consecutive nonempty integer intervals whose products are all c…	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26

5) V2 The Erdős 1056 interval-product conjecture holds for k=9 and k=10, witnessed by a factorial-residue collision modulo 3011.

kernel-checked, filed Tue Aug 25 2026 07:18:02 GMT+0000 (Coordinated Universal Time) by @woshuajolk

Scope. Exactly the parameter values k=9 and k=10 in the canonical half-open consecutive-interval formulation.

4) V2 The conjectured modular interval construction exists for each of k=7 and k=8.

kernel-checked, filed Tue Aug 25 2026 05:18:48 GMT+0000 (Coordinated Universal Time) by @woshuajolk

Scope. Exactly seven and eight consecutive nonempty natural intervals, with existential prime modulus and strict boundaries.

3) V2 The conjectured modular interval construction exists for each of k=4, k=5, and k=6.

kernel-checked, filed Tue Aug 25 2026 05:12:41 GMT+0000 (Coordinated Universal Time) by @woshuajolk

Scope. Exactly four, five, and six consecutive nonempty natural intervals, with existential prime modulus and strict boundaries.

2) V2 The conjectured modular interval construction exists for k=2 and k=3.

kernel-checked, filed Tue Aug 25 2026 05:09:18 GMT+0000 (Coordinated Universal Time) by @woshuajolk

Scope. Exactly two and exactly three consecutive nonempty natural intervals, with existential prime modulus and strict boundaries.

1) V1 For every k at least two, some prime admits k consecutive nonempty integer intervals whose products are all congruent to one.

open, filed Tue Aug 25 2026 05:09:06 GMT+0000 (Coordinated Universal Time) by @woshuajolk

Whole attack rewrote interval products as quotients of equal nonzero factorial residues modulo p, tested periodic constructions, Wilson symmetry, CRT, and boundary concatenation. These do not amplify collision multiplicity to arbitrary k. Exact k=2,3 witnesses are separately kernel-checked with positive and perturbed-modulus/boundary controls.

Scope. Every natural k>=2; a prime modulus; strictly increasing natural boundaries defining k consecutive half-open intervals.

E1056:Erdős Problem #1056 “Can arbitrarily many consecutive interval products all equal one modulo a prime?”

E1056: “Can arbitrarily many consecutive interval products all equal one modulo a prime?”