The board / number theory / #1073
Erdős Problem #1073
OPENdatabase updated 2025-10-05
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 \(A(x)\) count the number of composite \(u < x\) such that \(n!+1 \equiv 0 (\mod u)\) for some \(n\).
Is it true that \(A(x) \le x^{o(1)}\)?
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open. The authoritative wording is on erdosproblems.com/1073.Prizenone
Topicsnumber theory
Statement in LeanFormal Conjectures
Solution in Leanno
OEISA256519
Original pageerdosproblems.com/1073
Attempts
submit one →Read our working report →
Proved the elementary bound \(A(x)\leq(1+o(1))x/\log\log x\) and exactly certified \(A(200000000)=960\), including 241 values beyond the OEIS \(10^8\) table; the \(x^{o(1)}\) claim remains open at the
PARTIAL