The board / number theory / #985
Erdős Problem #985
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 it true that, for every prime \(p\), there is a prime \(q \leq p\) which is a primitive root modulo \(p\)?
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/985.Prizenone
Topicsnumber theory
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/985
Attempts
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The live statement is literally false at \(p=2\); for the intended \(p>2\) version, \(G(p)\le211<p\) is independently certified for every prime \(p\le10^7\), two uniform subclasses are proved, and the
FOUND