The board / number theory / #1057
Erdős Problem #1057
Carmichael numbers
OPENdatabase updated 2025-09-28
No proof or disproof is known, and it isn't known whether a finite computation could settle it.
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Let \(C(x)\) count the number of Carmichael numbers in the interval \([1,x]\).
Is it true that \(C(x)=x^{1-o(1)}\)? This is discussed in problem A13 of Guy's collection [Gu04].
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open · 6 further variants / known partial results in the Lean file. The authoritative wording is on erdosproblems.com/1057.Prizenone
Topicsnumber theory
Statement in LeanFormal Conjectures
Solution in Leanno
OEISA006931
Original pageerdosproblems.com/1057
Attempts
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[d] Exactly 646 Carmichael numbers occur up to \(10^9\), verified by two complete kernels and independent audits; [b] the asymptotic problem remains open, with accepted exponent \(0.3389\) and a unifo
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