What was already known
Related laws were known for other digit-defined families. Col and Dartyge–Rivat–Swaenepoel supplied distribution inputs used here; large-prime-factor counts of palindromes were a different result.
AI involvement
The author says Claude models helped develop the modified moment criterion with a finite exceptional-prime set, then drafted the manuscript and Lean development. The author checked the final statements and proofs.
The modified criterion is central new mathematical work developed jointly with the models; locating Col's prior theorem alone would not establish eligibility.
Importance
Establishes new typical prime-factor laws using a modified moment criterion with finitely many exceptional primes.
Limitations
The Lean derivation assumes eight transcribed literature inputs. Some source transcriptions were checked, but Col’s original input was not independently accessible in the public verification report.
Technical verification
The author reports checking all final statements and proofs, and a sorry-free Lean 4 development proves the paper's arguments conditional on eight explicitly transcribed literature results. Two paper-specific inputs were checked against originals, one via a secondary quotation, and Col's original was not independently accessible; that source-faithfulness gap remains explicit.
Formal checking
Author review of all statements, proofs and references
- Checker
- vibefrtz, pseudonymous paper author
- Scope
- Palindromic and reversed-prime Erdős–Kac theorems, proofs and cited references
- Basis
- Reported by the linked checker
Formal checking
Sorry-free Lean derivations with committed axiom audit
- Checker
- Lean 4/mathlib kernel on EKRev main theorems
- Scope
- Theorems 1.1 and 1.2, conditional on eight quoted literature inputs
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
The human author jointly developed the general criterion and reports verifying its proofs, documenting understanding of the central moment-and-distribution mechanism.
Correction and publication history
Establishes new typical prime-factor laws using a modified moment criterion with finitely many exceptional primes.
Read this published revision