Claims

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1998_01_01_chen: The Theorem of Chen's 1998 Acta Arithmetica paper gives g(N) ~ (9N/8)^{1/2}, the size of Erdős's construction, which answers the first question in the asymptotic form Erdős conjectured; refereed.

2007_01_01_chen_dai: Theorem 1(ii) of Chen and Dai's 2007 Acta Arithmetica paper gives, for infinitely many N, an admissible set larger than Erdős's construction by an unbounded amount, so the construction is not a largest set; refereed.

2026_06_19_axiommath: AxiomProver's Lean 4 file, posted to the site's thread in June 2026, exhibits N = 336 and a 21-element admissible set beating Erdős's 18-element construction; not built or audited here.

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