The board / number theory / #971
Erdős Problem #971
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).
`leastCongruentPrime a d` is the least prime congruent to `a` modulo `d`.
Let `p(a, d)` be the least prime congruent to `a (mod d)`. Does there exist a constant `c > 0` such that for all large `d`, `p(a, d) > (1 + c) * φ(d) * log d` for `≫ φ(d)` many values of `a`?
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open · 2 further variants / known partial results in the Lean file. The authoritative wording is on erdosproblems.com/971.Prizenone
Topicsnumber theory
Statement in LeanFormal Conjectures
Solution in Leanno
OEISA226521
Original pageerdosproblems.com/971
Attempts
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Live page status is OPEN, but it lists “1 claimed proof for this problem” (a partial proof claimed by KyungMin Han, submitted 2026-07-25 by Dogcake); “Currently working on this problem” is None.
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