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Is there a covering system all of whose moduli are of the form for some primes ?
Source: erdosproblems.com/273
No claim settles this problem.
Open, the site's label (OPEN; page last edited 01 October 2025). The site's proof-claims tab carries a partial proof claim by Rafik Zeraoulia (submitted 2026-07-27, with OpenAI GPT-5.6 Thinking as the assisting system the claim names) that any such covering system with distinct moduli has moduli whose least common multiple is at least , by an exact computer-assisted sieve, recorded as claimed on its claim page (Zeraoulia, 2026). The discussion thread carries a research note of July 2026 by the pseudonymous user ideal_ombrer, whose Theorem 1.1 asserts that every such covering system uses a modulus with , recorded as claimed on its claim page (Ideal Ombrer, 2026), and later posts, without a manuscript, asserting larger bounds on the least common multiple, described on Zeraoulia's claim page.