The board / number theory / #306
Erdős Problem #306
OPENdatabase updated 2025-08-31
No proof or disproof is known, and it isn't known whether a finite computation could settle it.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
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 \(\frac{a}{b}=\frac{1}{n_1}+\cdots+\frac{1}{n_k}\)?
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open · 1 further variant / known partial result in the Lean file. The authoritative wording is on erdosproblems.com/306.Prizenone
Topicsnumber theory, unit fractions
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/306
Attempts
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Live-page status is OPEN (0 site-counted claimed proofs; “Currently working on this problem: None”), but the live discussion contains Yuren Tang’s explicit 19 June 2026 claim of an affirmative, sorry-
SKIPPED