The board / number theory / #1203
Erdős Problem #1203
OPENdatabase updated 2026-04-04
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).
If \(\omega(n)\) counts the number of distinct prime divisors of \(n\) then let \(F(n)=\max_k \omega(n+k)\frac{\log\log k}{\log k}.\)
Prove that \(F(n)\to \infty\) as \(n\to \infty\).
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open · 1 further variant / known partial result in the Lean file. The authoritative wording is on erdosproblems.com/1203.Prizenone
Topicsnumber theory
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/1203
Attempts
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Live page status is OPEN with 0 claimed proofs, but idrissbado is listed under “Currently working on this problem”; the mandatory collision rule therefore requires no attempt.
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