A proof of the Erdős primitive set conjecture · HackerPapers discussions

A proof of the Erdős primitive set conjecture — mentioned by tromp

Sat, 13 May 2023 07:37:19 GMT

This appears as the 2nd-last solved conjecture on the List of conjectures by Paul Erdős [1] with 3 references, the first being Jared's paper [2], the 2nd a quanta magazine article [3] and the 3rd this Numberphile video. [1] https://en.wikipedia.org/wiki/List_of_conjectures_by_Paul_Er... [2] https://arxiv.org/abs/2202.02384 [3] https://www.quantamagazine.org/graduate-students-side-projec...

Paper and discussion history. A mention is not an endorsement.

A proof of the Erdős primitive set conjecture — mentioned by dragon96

Tue, 07 Jun 2022 00:16:33 GMT

For anyone interested in a more technical summary of the some of the main ideas: Problem Statement The Erdos conjecture that all primitive sets S satisfy f(S) <= f(PRIMES), where f(S) = sum_{s} (1/(s log s)) and PRIMES is the set of all primes. Definitions Define A_q to be a primitive set such that all elements a are divisible by prime q, but no primes less than q. * Example: A_3 contains multiples of 3, but no even numbers. Define A*_q to be the set of all integers divisible by only primes >= q. * Example: A_q is a subset of A*_q. * Example: A_q is also a subset of q \* A*_q (i.e. multiply…

Paper and discussion history. A mention is not an endorsement.

A proof of the Erdős primitive set conjecture — mentioned by rob_c

Mon, 06 Jun 2022 23:13:22 GMT

For anyone who speaks maths https://arxiv.org/abs/2202.02384 Unfortunately without a maths UG it's a hard slog I'll agree, but not the most impenetrable paper over ever seen. Not going to pretend I get the subtleties though.

Paper and discussion history. A mention is not an endorsement.

A proof of the Erdős primitive set conjecture — mentioned by nabla9

Mon, 06 Jun 2022 16:54:51 GMT

> Mathematicians noted that the work is particularly striking because it relies entirely on elementary arguments. “It wasn’t like he was waiting for all this crazy machinery to develop,” Thompson said. “He just had some really clever ideas.” the proof: https://arxiv.org/pdf/2202.02384.pdf Last time I saw something so simple that I think I could understand the idea because it has not too many new concepts was Hao Huang Sensitivity Conjecture: http://www.mathcs.emory.edu/~hhuan30/papers/sensitivity_1.pd... Donald Knuth further simplified it into one page…

Paper and discussion history. A mention is not an endorsement.

A proof of the Erdős primitive set conjecture — mentioned by Victerius

Mon, 06 Jun 2022 16:15:10 GMT

Link to Arxiv pre-print: https://arxiv.org/abs/2202.02384

Paper and discussion history. A mention is not an endorsement.