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Erdős Problem #793: the second-order constant for strongly 2-primitive sets

The preprint claims that the maximum size F(n) is π(n) + (27/2 + o(1))n^(2/3)/(log n)^2. It gives matching upper and lower bounds, and a public Lean package encodes the same constant and allows the two factors in the divisibility condition to coincide.

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Stable ID
math-erdos-793-strongly-two-primitive-2026
Revision
math-erdos-793-strongly-two-primitive-2026.v1
Field
Mathematics · Number theory and formal mathematics
Evidence
Tier 1 · Peer reviewed: No
Record state
Provisional · Lean-checked claim; specialist review pending
Last checked

AI role

Chojecki's paper discloses AI assistance in exploring the argument and writing the text. The Erdős Problems record credits GPT-5.6 Sol, prompted by Chojecki, with the solution; the separate Lean archive describes an AI-generated formal proof and a human-operated audit.

Record details

Problem or result
Erdős Problem #793, asking whether the extremal size of a strongly 2-primitive subset of {1,…,n} has a constant second-order term
Authors
Przemek Chojecki (sole listed author); GPT-5.6 Sol credited in the project record
Institutions
Ulam AI
Result date
Preprint and Lean artifact posted July 14, 2026

Why it matters

The formula identifies the exact second-order constant in an Erdős extremal-number-theory problem whose order of growth was known but whose asymptotic constant was not.

Limits

This is a first-version, non-peer-reviewed proof without located independent specialist assessment. Erdős Problems marks it PROVED (LEAN) while its external metadata still says the statement is not formalized. The self-published Star Fleet Math bundle contains the proof sources and build logs, but omits the pinned external dependency directories referenced by its verifier, so the exact build could not be replayed locally from the ZIP alone. The archive operator reports a clean rebuild; this tracker therefore records a Lean-checked claim, not field acceptance.

Sources

  1. Primary: Przemek Chojecki, The Second Term for Strongly 2-Primitive Sets
  2. Primary: Erdős Problems #793 record and status history
  3. Primary: Star Fleet Math self-published verification report
  4. Primary: Star Fleet Math public Lean solution bundle

Correction and revision history

  1. 2026-07-23 — Added after the human-proof preprint, exact Lean statement, public proof sources and archive audit became inspectable; retained as provisional because specialist review and an independently reproducible complete dependency bundle were not located.

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