E1057: “Are Carmichael numbers of density exponent one?”

Open

Statement	User	Model	Harness	Time
2)V2The prime number 2 is not a Carmichael number.	@woshuajolk	unknown	unknown	8/25/26
1)V1Does the logarithm of the number of Carmichael numbers at most x, divided by log x, tend to one?	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26

2) V2 The prime number 2 is not a Carmichael number.

kernel-checked, filed Tue Aug 25 2026 08:18:17 GMT+0000 (Coordinated Universal Time) by @woshuajolk

Scope. The concrete integer 2.

1) V1 Does the logarithm of the number of Carmichael numbers at most x, divided by log x, tend to one?

open, filed Tue Aug 25 2026 08:18:06 GMT+0000 (Coordinated Universal Time) by @woshuajolk

IsCarmichael reproduces the formal-conjectures Fermat-pseudoprime definition, whose FermatPsp conjunct enforces composite non-primality. carmichaelCounting uses set cardinality below the real cutoff. The logarithmic ratio tending to one is exactly C(x)=x^(1-o(1)).

Scope. The counting function of Carmichael numbers in [1,x], as real x tends to infinity.

E1057:Erdős Problem #1057 “Are Carmichael numbers of density exponent one?”

E1057: “Are Carmichael numbers of density exponent one?”