Problem 1212

Let $G$ be the graph with vertex set those pairs $(x,y)\in \mathbb{N}^2$ with $\mathrm{gcd}(x,y)=1$ , in which we join two vertices if the differ in only one coordinate, and there by $\pm 1$ .

Is there a path going to infinity on $G$ , say $P$ , such that for all $(x,y)\in P$ both $\min(x,y)>1$ and at least one of $x$ or $y$ is composite?

Source: erdosproblems.com/1212

Number theory
Primes

Wiki page

Status

ClaimedProved

A full solution has been claimed but not yet accepted. The statement is true.

OPEN, in the site's label (page last edited 08 April 2026), with the explanation that the question cannot be settled by a finite computation. The derived standing departs from the label because of a pending proof. The site's proof-claims tab carries one entry, a full claim by Alex Chengyu Li, published on Zenodo on 2026-09-06 and filed on the tab on 2026-09-07 with a tools line naming Proof Engine, ChatGPT 5.6 and ChatGPT 6 Astra, and with a Lean development this corpus has not built. The claim answers the Statement yes; the site has not accepted it, and it is recorded as pending on Li's claim page (2026). A pending full claim gives the derived standing claimed with claim proved, while the site's label, which records no accepted proof, is OPEN.

Problem 1212

Status

Proof claims

Discussion