Decomposing factorial of 300K as the product of 300K factors larger than 100K

http://gus-massa.blogspot.com/2025/04/decomposing-factorial-of-300k-as.html

by gus_massa • 1 year ago

97 9 1 year ago

gus-massa.blogspot.com

pvg• 1 year ago

HN thread for the Tao piece https://news.ycombinator.com/item?id=43506238

hansvm• 1 year ago

A mathy construction like in the article is probably important for the full conjecture, but isn't this concrete case just an instance of the bin-covering problem? Your discrete items are the log of each prime factor (included according to its multiplicity), set the lower threshold to log(100k), and if you get any solution with 300k or more factors, you can redistribute the extra factors arbitrarily.

madcaptenor• 1 year ago

Tao agrees with you: https://terrytao.wordpress.com/2025/03/26/decomposing-a-fact...

btilly• 1 year ago

In the same thread Tao commented https://terrytao.wordpress.com/2025/03/26/decomposing-a-fact... which shows work from Andrew Sutherland that got the 100k limit after about a day.

As impressed as I am with this solution, it didn't get to be the first to solve the problem.

keepamovin• 1 year ago

I like how Tao put out the call, and you answered it. Very cool! I was waiting for someone on here with engineering and math chops to attempt devising a more efficient approach teased in that article. Super cool to see you do it! You might be co-author on his paper, I think that's what he said, hahaha ! :)

ashton314• 1 year ago

Hey! This guy is using the fancy new treelist [1] package which implements RRB trees. These are super cool data structures: a cache-friendly, multiway tree structure to store a sorted collection with O(log_{32} n) read, functional insert/update/append/prepend. Really a fantastic data structure for functional programming.

[1] https://docs.racket-lang.org/reference/treelist.html

spdegabrielle• 1 year ago

This was added for Rhombus - where it is the default.

https://rhombus-lang.org/

Decomposing factorial of 300K as the product of 300K factors larger than 100K

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