The board / number theory / #279
Erdős Problem #279
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).
Let \(k\geq 3\). Is there a choice of congruence classes \(a_p\pmod{p}\) for every prime \(p\) such that all sufficiently large integers can be written as \(a_p+tp\) for some prime \(p\) and integer \(t\geq k\)?
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open. The authoritative wording is on erdosproblems.com/279.Prizenone
Topicsnumber theory, covering systems, primes
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/279
Attempts
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Rigorous reduction to boundedness of H_k, FGKMT-based sublinear bound, repaired density-one proof, and independently verified exact frontier H_3(172)=76; the required uniform O(1) bound remains open.
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