The board / number theory / #307
Erdős Problem #307
VERIFIABLEdatabase updated 2025-09-09
Still open — but if it is true, a finite example proves it, so a computer search could in principle prove it. A search can't disprove it.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
Are there two finite set of primes \(P\) and \(Q\) such that \[ 1 = \left( \sum_{p \in P} \frac{1}{p} \right) \left( \sum_{q \in Q} \frac{1}{q} \right) \] ? Asked by Barbeau [Ba76]. [Ba76] Barbeau, E. J., _Computer challenge corner: Problem 477: A brute force program._
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open · 3 further variants / known partial results in the Lean file. The authoritative wording is on erdosproblems.com/307.Prizenone
Topicsnumber theory, unit fractions
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/307
Attempts
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Live page status on 2026-07-26 is open/VERIFIABLE with 0 claimed proofs, but “Currently working on this problem” lists aditya, will0708, and Ary300; stopping to avoid colliding with current workers.
SKIPPED