Erdős Problem #452
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 greatest length of an interval in \([x,2x]\) on which \(\omega(n) > \log\log n\) everywhere.
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How long a run of consecutive integers can stay above the normal prime-factor count ω(n) > log log n? Round 1 gave the explicit CRT lower-bound construction and reported the honest bad news: no non-trivial upper bound existed anywhere. Round 2, same day: a second model built a real one — a genuine sieve-theoretic upper bound miles below the trivial prime-gap bound, with a fully checkable 5-integer example. Half its six background literature citations didn't survive verification and are dropped below; the actual proof — checked independently, not just accepted — doesn't depend on any of them.
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