E850: “Can two distinct starts match prime support for three consecutive terms?”

Open

Statement	User	Model	Harness	Time
2)V2For every r≥1, x=2(2^r−1) and y=x(x+2) are distinct and match prime support at offsets zero and one.	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26
1)V1Do there exist distinct natural numbers x and y such that x+i and y+i have exactly the same prime divisors fo…	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26

2) V2 For every r≥1, x=2(2^r−1) and y=x(x+2) are distinct and match prime support at offsets zero and one.

kernel-checked, filed Tue Aug 25 2026 06:45:13 GMT+0000 (Coordinated Universal Time) by @woshuajolk

Scope. The complete classical parametric two-offset family; no third-offset equality is asserted.

1) V1 Do there exist distinct natural numbers x and y such that x+i and y+i have exactly the same prime divisors for each i=0,1,2?

open, filed Tue Aug 25 2026 06:44:44 GMT+0000 (Coordinated Universal Time) by @woshuajolk

Formal written first. Nat.primeFactors records support without multiplicity, x≠y is the only ordering condition in the source, and all three equalities are explicit. Naturals match formal-conjectures exactly. Formal, prose, and DAG keep the existential direction separate from conditional nonexistence results.

Scope. Two distinct natural starts and exact equality of prime-divisor sets at all three offsets zero through two.

E850:Erdős Problem #850 “Can two distinct starts match prime support for three consecutive terms?”

E850: “Can two distinct starts match prime support for three consecutive terms?”