The board / number theory / #398
Erdős Problem #398
Brocard-Ramanujan conjecture
FALSIFIABLEdatabase updated 2025-08-31
Still open — but if it is false, a finite counterexample exists, so a computer search could in principle disprove it. A search can't prove it.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
**Brocard's Problem** Does \(n! + 1 = m^2\) have integer solutions other than \(n = 4, 5, 7\)?
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open. The authoritative wording is on erdosproblems.com/398.Prizenone
Topicsnumber theory, factorials
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/398
Attempts
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The live page displays the problem as FALSIFIABLE/open, with 0 site-filed claimed proofs and no current worker, but its comments list Ahmad Sabihi's paper “A short solution for Brocard-Ramanujans’ pro
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