Erdős Problem #1188

Erdős problem #1188 · erdosproblems.com/1188

Estimate the number $F(x)$ of minimal distinct covering systems whose moduli all lie in $[1, x]$. The candidate proof gives $\log\log F(x)/\log x \to 1$, i.e. $F(x) = \exp(x^{1+o(1)})$.

Result

Proved

Status

Candidate (review pending)

AI contribution

AI-discovered

Method

Argument

Field

Number Theory, Covering Systems

Posed by

—

Year posed

—

Years open

—

Solved

2026-07-13

Model

GPT-5.6 starships (Claude Fable 5 reviewer)

Vendor

OpenAI / Anthropic

Collaborators

—

Verification

Lean-verified

Publication

Announced

Significance

10 / 100*

Disclosed cost

—

Wikipedia

No dedicated article