The board / number theory / #850
Erdős Problem #850
Erdős-Woods conjecture
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).
Can there exist two distinct integers \(x\) and \(y\) such that \(x,y\) have the same prime factors, \(x+1,y+1\) have the same prime factors, and \(x+2,y+2\) also have the same prime factors?
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open. The authoritative wording is on erdosproblems.com/850.Prizenone
Topicsnumber theory, primes
Statement in LeanFormal Conjectures
Solution in Leanno
OEISA343101
Original pageerdosproblems.com/850
Attempts
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elementary reduction and an independent exact scan exclude y<=10^9; modulo Hercher's published exhaustive Theorem 1, all y<1.4e12 are excluded, but the unbounded problem remains open.
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