The board / number theory / #421
Erdős Problem #421
SOLVEDdatabase updated 2025-08-31
Resolved in some way other than a straight proof or disproof — usual for open-ended questions, or for multi-part problems whose parts went different ways.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
There exists a sequence \(1 \le d_1 < d_2 < \dots\) with density 1 such that all products \(\prod_{u \le i \le v} d_i\) are distinct. This was solved affirmatively; see [Pratt26].
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research solved. The authoritative wording is on erdosproblems.com/421.Prizenone
Topicsnumber theory
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/421
Attempts
submit one →Remote-witness obstruction unresolved; a blind reattempt corroborated the architecture, no summable bound.
WALL