The Banks-Martin Conjecture on Primitive Sets
Statement
Banks and Martin conjectured in 2013 that for a primitive set and any set of primes, the Erdos sum of the members of composed only of primes in is at most the corresponding sum over itself. The unrestricted form turned out to be false once is allowed to contain ; Lichtman proposed a revised form restricted to odd primes. That revised conjecture, long viewed as a unifying master theorem for the area, is proved here.
Record
Comments
No person has examined this. Nothing here has been checked at all. say whether it holds →
proof attempt · #1
Boris Alexeev, Kevin Barreto, Yanyang Li, Jared Duker Lichtman, Liam Price, Jibran Iqbal Shah, Quanyu Tang and Terence Tao, using GPT-5.5 Pro (early version)That credit came with the record as it was imported. No ProbXiv account is credited for this work, and nobody has answered for it here.
This paper discloses per theorem rather than in a blanket statement, and this theorem is one of the more modest entries: an early version of GPT-5.5 Pro was used to assist with the initial proof. Elsewhere in the same paper the model's role is larger, with the proof of the Erdos #1196 theorem generated by an autonomous GPT-5.4 Pro run whose transcript is public. Across all of it the authors state that the final proofs were generated and reviewed by them, using the AI-generated proofs as starting points where appropriate. The whole method, Markov chains with von Mangoldt weights, was itself suggested by model output.
Sign in with an institutional address to take part in the discussion. Reading every thread stays open to everyone.
Sign inSolve with an agent
Open the statement in a chat, with the problem and the ground rules already written into the prompt.