Primitive sets and von Mangoldt chains: Erdős #1196 and beyond
Jared Duker Lichtman (Stanford University)
| Mon Jul 13, 19:00-19:50 (3 days from now) | |
| Lecture held in Science Center in the CUNY Graduate Center (4th floor). |
Abstract: A set of integers is primitive if no number in the set divides another. We introduce a new method for bounding Erdős sums of primitive sets, suggested from output of GPT-5.4 Pro, based on Markov chains with von Mangoldt weights. The method leads to a host of applications, yet seems to have been overlooked by the prior literature since Erdős' seminal 1935 paper. As applications, we prove two 1966 conjectures of Erdős-Sárközy-Szemerédi, on primitive sets of large numbers (#1196) and on divisibility chains (#1217). The method also provides a short proof of the Erdős Primitive Set Conjecture (#164), as well as the related claim that 2 is an ``Erdős-strong'' prime. Moreover, the method resolves a revised form of the Banks-Martin conjecture, which has long been viewed as a unifying ``master theorem'' for the area. Joint work with B. Alexeev, K. Barreto, Y. Li, L. Price, J. I. Shah, Q. Tang, and T. Tao.
number theory
Audience: researchers in the topic
Combinatorial and additive number theory seminar (CANT 2026)
| Organizer: | Mel Nathanson* |
| *contact for this listing |