The board / number theory / #383
Erdős Problem #383
OPENdatabase updated 2025-08-31
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).
Is it true that for every \(k\) there are infinitely many primes \(p\) such that the largest prime divisor of \[ \prod_{i = 0}^k (p ^ 2 + i) \] is \(p\)?
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open. The authoritative wording is on erdosproblems.com/383.Prizenone
Topicsnumber theory
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/383
Attempts
submit one →Read our working report →
Live page status is OPEN with 1 claimed proof—a partial proof claimed by Rafik Zeraoulia and submitted 2026-07-25—while “Currently working on this problem” is None (accessed 2026-07-28); the mandatory
SKIPPED