The board / number theory / #770
Erdős Problem #770
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 \(h n\) be the minimal number such that \(2 ^ n - 1, \dots, h(n) ^ n - 1\) are collectively coprime.
For every prime `p`, does the density of integers with `h n = p` exist?
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open · 3 further variants / known partial results in the Lean file. The authoritative wording is on erdosproblems.com/770.Prizenone
Topicsnumber theory
Statement in LeanFormal Conjectures
Solution in Leanno
OEISA263647
Original pageerdosproblems.com/770
Attempts
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Live page status OPEN; it lists 1 claimed proof (a partial proof claimed by Jeffrey Zeng, submitted 2026-07-24 17:13:29) and no current worker, so the mandatory no-duplication rule applies.
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