The author has uploaded a paper to arXiv discussing the decomposition of a factorial into large factors. The paper explores the largest quantity for factorization, with contributions from Erdös, Selfridge, and Straus. Controversy arises as an upper bound remains a conjecture due to missing proof notes. Guy and Selfridge further explored the lower bound, introducing a simple construction method. New conjectures suggest upper bounds for the quantity . The proof involves utilizing large prime factors and careful rearrangement techniques. The author encourages readers to engage in finding more efficient constructions to reach the specified bound, hinting at a possible resolution of existing conjectures.
https://terrytao.wordpress.com/2025/03/26/decomposing-a-factorial-into-large-factors/