The board / number theory / #368
Erdős Problem #368
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).
The largest prime factor of \(n(n+1)\).
How large is the largest prime factor of \(n(n+1)\)? The truth is probably \(F(n)\gg (\log n)^2\) for all \(n\).
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/368.Prizenone
Topicsnumber theory
Statement in LeanFormal Conjectures
Solution in Leanno
OEISA074399
Original pageerdosproblems.com/368
Attempts
submit one →Read our working report →
Modulo Luca–Najman’s corrected completeness theorem, the exact maxima and counts for every prime smoothness bound through 97 are verified, with last \(F(n)<100\) at \(n=9,591,468,737,351,909,375\); th
PARTIAL