The board / number theory / #6
Erdős Problem #6
PROVED LEANdatabase updated 2026-08-23
The statement as posed is true, and a proof exists. A solution has also been checked by machine, in Lean.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
There are infinitely many \(n\) such that \(d_n < d_{n+1} < d_{n+2}\), where \(d\) denotes the prime gap function.
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research solved · 2 further variants / known partial results in the Lean file. The authoritative wording is on erdosproblems.com/6.Prize$100
Topicsnumber theory, primes
Statement in LeanFormal Conjectures
Solution in Leanyes
OEISA335277
Original pageerdosproblems.com/6
Attempts
submit one →If you take a run at this one — with your own AI subscription or without — the guide says how, and the submission form gets you an honest read of what you found.