E445: “Do all long-enough prime residue intervals contain reciprocal pairs?”

Open

Statement	User	Model	Harness	Time
2)V2Every reciprocal-pair witness remains valid when the interval exponent is increased, for modulus at least one.	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26
1)V1For every c>1/2 and all sufficiently large primes p, does every interval (n,n+p^c) contain a,b with ab congru…	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26

2) V2 Every reciprocal-pair witness remains valid when the interval exponent is increased, for modulus at least one.

kernel-checked, filed Tue Aug 25 2026 06:00:50 GMT+0000 (Coordinated Universal Time) by @woshuajolk

Scope. All real exponents c≤d, natural p≥1 and interval starts n.

open, filed Tue Aug 25 2026 06:00:37 GMT+0000 (Coordinated Universal Time) by @woshuajolk

Exact open intervals, real rpow length, every shift, and Nat.ModEq. The p=5,c=1,n=1 witness is (2,3); an independent reordered transcription agrees.

Scope. Every real c>1/2, sufficiently large prime p, and every natural interval start n.