Decomposing factorial of 300K as the product of 300K factors larger than 100K
9 comments
·April 8, 2025hansvm
madcaptenor
Tao agrees with you: https://terrytao.wordpress.com/2025/03/26/decomposing-a-fact...
btilly
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.
gus_massa
I did't notice it. It's using a different method, but it's interesting that it also uses the primes in N! ordered from bigger to smaller.
keepamovin
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 ! :)
pvg
HN thread for the Tao piece https://news.ycombinator.com/item?id=43506238
ashton314
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.
spdegabrielle
This was added for Rhombus - where it is the default.
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.