The board / number theory / #689
Erdős Problem #689
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 `n` be sufficiently large. Is there some choice of congruence class `a_p` for all primes `2 ≤ p ≤ n` such that every integer in `[1,n]` satisfies at least two of the congruences `≡ a_p (mod p)`? Yes: this follows from the greedy-matching reduction of Chojecki [Ch26] combined with an unconditional Fourier-analytic proof of the required three-prime counting estimate.
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research solved. The authoritative wording is on erdosproblems.com/689.Prizenone
Topicsnumber theory
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/689
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