The board / number theory / #273
Erdős Problem #273
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).
Is there a covering system all of whose moduli are of the form \(p-1\) for some primes \(p \geq 5\)?
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open · 1 further variant / known partial result in the Lean file. The authoritative wording is on erdosproblems.com/273.Prizenone
Topicsnumber theory, covering systems
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/273
Attempts
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Live page status OPEN (accessed 2026-07-28); it lists “1 claimed proof for this problem,” specifically a partial proof claimed by Rafik Zeraoulia using OpenAI GPT-5.6 Thinking and submitted 2026-07-27
SKIPPED