The board / number theory / #961
Erdős Problem #961
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).
Sylvester and Schur [Er34] proved that every set of \(k\) consecutive integers greater than \(k\) contains an integer divisible by a prime greater than \(k\), i.e. not \((k+1)\)-smooth.
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research solved · 4 further variants / known partial results in the Lean file. The authoritative wording is on erdosproblems.com/961.Prizenone
Topicsnumber theory
Statement in LeanFormal Conjectures
Solution in Leanno
OEISA213253
Original pageerdosproblems.com/961
Attempts
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live gate cleared; proved the quantitative binomial reduction, independently certified exact f(k) for k<=40 modulo the Carmichael-Lehmer cutoff, and constructed f(647134389)>=288; the uniform exponent
PARTIAL