The board / number theory / #4
Erdős Problem #4
PROVEDdatabase updated 2025-08-31
The statement as posed is true, and a proof exists.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
Is it true that, for any \(C > 0\), there infinitely many \(n\) such that: \[ p_{n + 1} - p_n > C \frac{\log\log n\log\log\log\log n}{(\log\log\log n) ^ 2}\log n \]
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research solved · 1 further variant / known partial result in the Lean file. The authoritative wording is on erdosproblems.com/4.Prize$10,000
Topicsnumber theory, primes
Statement in LeanFormal Conjectures
Solution in Leanno
OEISA002386
Original pageerdosproblems.com/4
Attempts
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