Erdős Problem #872
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).
A primitive subset of \(\{2, \dots, n\}\) is a set in which no element divides another. The quantified divisibility condition is one-sided because the variables range over all ordered pairs of distinct elements.
A game position consists of the already claimed set and the still unclaimed pool.
The legal moves from a position: unclaimed elements whose insertion preserves primitiveness.
Attempts
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The authoritative live page (accessed 2026-07-27; status OPEN; 0 claimed proofs) lists current workers old-bielefelder, pommeret, and joshoakley, so the mandatory non-collision rule requires no attemp
SKIPPED