Claim in Erdős problems named in new papers, 2026-10

A published paper or arXiv preprint answers the main question of Erdős Problem #306 (theorem erdos_306 in formal-conjectures) in full (proof, disproof, or the exact value asked for) with no hypotheses beyond the problem's own.

Problem as stated at github.com/google-deepmind/formal-conjectures/blob/34ee0e3c5fd52d202d62a71094a37970cb5fb870/FormalConjectures/ErdosProblems/306.lean. The claim text is written by Corroborate; that site has not reviewed or endorsed it.

The problem, as stated in formal-conjectures (Apache 2.0):

Let \frac a b\in \mathbb{Q}_{>0} with b squarefree. Are there integers 1 < n_1 < \dots < n_k, each the product of two distinct primes, such that \frac{a}{b}=\frac{1}{n_1}+\cdots+\frac{1}{n_k}?

References formal-conjectures lists for this problem (a starting point, not evidence):

[Ta26] Tang, Yuren, A Lean 4 formalisation of Erdős Problem 306, which derives the statement below from two results of Rosser and Schoenfeld, Approximate formulas for some functions of prime numbers, Illinois J. Math. *6* (1962), 64-94, declared there as axioms

Verdict: no verdict yet

Evidence for

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Evidence against

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New papers that mention this problem

Unit fractions with semiprime denominators: an elementary proof of Erdős Problem #306Shisheng Li · 2026-09-26 · a lead, not a verified resultAppears in the erdosproblems.com proof-claims thread for this problem (automatic text match; check the thread).