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Claim. The answer to Problem 279, read with least residues, is yes: for every integer $k\ge3$ there are residues $0\le r_p<p$, one for each prime $p$, and an $N$ such that every $n\ge N$ equals $r_p+tp$ for some prime $p$ and some integer $t\ge k$. This is Theorem 1.1 of Wanfang Chen, One residue class modulo each prime can cover every sufficiently large integer, posted on 2026-07-28 with a Lean 4 development in the repository linked above. The paper states that the proof was generated by OpenAI's GPT-5.6-sol model, operating as Codex, and that the named author takes responsibility for it. Its construction uses a large hub prime $h$, the multiplicative semigroup generated by the primes congruent to $1$ modulo $h$, and a deterministic sieve that assigns new residue classes without undoing earlier coverage. The development's final theorem, Erdos279.globalAffirmative, states the claim for every $k\ge3$ with least residues, and the repository reports that it depends only on propext, Classical.choice and Quot.sound.

Depends on. Nothing in this wiki.

Standing. Claimed: no journal publication, referee report or curator ruling is recorded, and the site labels the problem OPEN (page last edited 17 April 2026). On the site's discussion thread on 2026-09-05, Johan Land pointed to the work and wrote that it seems to be a complete and unconditional proof, but that the work needs significant improvement and its Lean proof departs substantially from the manuscript; a forum comment is not acceptance. This corpus has not built or audited the development, so it gives no formalized evidence.