Research notes on every problem, and a library of the papers behind them. Built from the open erdos repository.
Updated
Claim. Michael Schroeder's Seven Prime Divisors in Odd Distinct Covering Systems asserts that the least common multiple of the moduli of any finite covering system with distinct odd moduli greater than one has at least 7 distinct prime divisors.
Covers. The negative answer to Problem 7 for periods with at most 6 prime divisors, regardless of exponents. It leaves periods involving more primes untreated and does not resolve the unrestricted question.
Standing. Claimed. The dated description on the author's research page and the forum announcement were read on 2026-10-16. They report a Lean formalization and supporting exact certificates. Neither the proof nor the formalization has been checked here, and no independent review or journal acceptance was located in those records. The date in this page's name is the paper date stated on the author's page; the linked manuscript was not read.
Depends on. Nothing in this wiki. No claim of an audited dependency chain is made.
Submission note. The author announced the seven-, eight- and nine-prime results together in the problem's discussion on 2026-09-15.