Erdős Problem #451
Prior state unknown→proved
the conjectured superpolynomial growth is established; the sharper order remains open
SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review
number-theory / Number Theory, Primes
Erdős Problem #451
Let $n_k$ be the least integer greater than $2k$ for which $\prod_{i=1}^k (n_k - i)$ has no prime factor in $(k, 2k)$. How rapidly must $n_k$ grow?
10Significance / 100
1Frontier events
0Verification tasks
0Recorded attempts
Temporal state
Current frontier
No reconciled state yet.
Append-only history
Frontier timeline
Research memory
Claims and attempts
Scoped claims
Let $n_k$ be the least integer greater than $2k$ for which $\prod_{i=1}^k (n_k - i)$ has no prime factor in $(k, 2k)$. How rapidly must $n_k$ grow?
the conjectured superpolynomial growth is established; the sharper order remains open
Recorded attempts
Evidence graph
Connected research record
No public relationships recorded yet.