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

97 pointsposted 7 months ago
by gus_massa
(gus-massa.blogspot.com)

9 Comments

hansvm

7 months 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

7 months ago

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

btilly

7 months 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.

gus_massa

7 months ago

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.

adgjlsfhk1

7 months ago

the primes bigger than ~sqrt(t) have an "obviously" best matching so it's not too surprising.

keepamovin

7 months 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

7 months 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