The board / number theory / #456
Erdős Problem #456
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 \(p_n\) be the smallest prime \(\equiv 1\pmod{n}\).
Let \(m_n\) be the smallest integer such that \(n\mid \phi(m_n)\).
Is it true that \(m_n<p_n\) for almost all \(n\)?
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open · 5 further variants / known partial results in the Lean file. The authoritative wording is on erdosproblems.com/456.Prizenone
Topicsnumber theory
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/456
Attempts
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Live page status is OPEN (0 formally listed claimed proofs; currently working: None), but the live discussion has a 4 May 2026 comment by DavidTurturean explicitly claiming an unconditional solution o
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