Busy Beaver Discuss

I'm starting a new monthly article series, This Month in Beaver Research (TMBR, pronounced "

Note that the previous 10^^(10^7) champion has been verified in Coq (https://github.com/ccz181078/

Pavel found an Ackermann level BB(7) TM last weekend. I evaluate that it halts with a sigma score

Racheline from bbchallenge Discord has discovered a TM which has a 5% chance to beat the current BB(6

Nice! Here are some rules for this TM: D(a, d) = 0^inf <C 0^a 1 2^d 1 0^inf D(a, d+3) --> D(2^{

The TM 0RB1RZ0RB_1RC1LB2LB_1LB2RD1LC_1RA2RC0LD was found by Pavel Kropitz back in May 2024 along with

Great find Andrés! A couple notes: The terminology "num(5)" comes from (Ben-Amram AM,

You're very welcome. Hope to “see” you on the discord! Sent by modern magic - TJL On Feb 6, 2025,

(1) Erratum: the first overflow rule should be 0 (11)^(x + 2) <A (23)^(y + 2) 0^3 --( 4x + 8y + 53

Hey, I'm really late to the party but it was great to see what you've been working on and

It turns out that many TMs (including the BB(5) and BB(2,4) champions) all simulate equivalent

I have computed that t_1(n,e) = (16(4^n - 1)/3) e^2 + ((4^(n + 3) - 28)/3 - 3 x 2^(n + 2)) e + (4^(n

@mxdys has adapted their BB(5) Coq proof to show that S(2,4) = 3932964: https://www.sligocki.com/2024

Also, Blog post by Scott Aaronson about the new result: https://scottaaronson.blog/?p=8088 HackerNews

"I'm saddened by this..." On Wed, May 29, 2024 at 2:36 PM Terry Ligocki <tjligocki@

sorry for the wasted effort. i've brushed up the code and fixed the bug and the good news is that

Ug, the spammers joined the group! I have added more restrictions including users having to request

I give here more analysis of this (3,3) machine. If A(a,b,c) = ...0(12)^a (11)^b < A (11)^c 0...,

I have often heard about Milton Green's 1964 TMs, but found it hard to understand their behavior

Pascal, you inspired me to dig a little more into this TM! I also found it hard to characterize the

I am delighted to report that my simulator is now able to verify Shawn's 10^^70 TM. The other big

My webpages about busy beavers are no longer at https://webusers.imj-prg.fr/~pascal.michel/index.html

I give here more analyses on the Turing machine p3 found by Pavel Kropitz on May 19, 2023, with s(p3)

Pavel Kropitz found a 3-state, 4-symbol TM which scores > 10↑↑2048! He originally shared it on the

Thanks Heiner, this is very interesting. I especially like how they have made a standard way to

Also, we may only be finding Collatz-like behavior in the BB candidates because it is one of the more

Long ago when I started looking for Busy Beavers, my Dad and I tried using Simulated Annealing: https

You're right, there's some kind of type error in what I'm trying to say. On the other

It seems that my website is no more available at its old address www.logique.jussieu.fr/~michel/ and

I think it's entirely possible already that G < BB(6). G is a huge number of course, but it