Groups
Groups
Sign in
Groups
Groups
Busy Beaver Discuss
Conversations
About
Send feedback
Help
Busy Beaver Discuss
Contact owners and managers
1–30 of 56
Mark all as read
Report group
0 selected
Pascal Michel
2
3:43 AM
An analysis of BMO1
More computations give: k N(k) N(k) - 2 x 3^(k - 1) 12 322659 -31635 13 959195 -103687 14 2840775 -
unread,
An analysis of BMO1
More computations give: k N(k) N(k) - 2 x 3^(k - 1) 12 322659 -31635 13 959195 -103687 14 2840775 -
3:43 AM
Tristan Stérin
Sep 17
BB5 arXiv release
Hello everyone, We've released the BB5 paper on arXiv: https://arxiv.org/pdf/2509.12337 Have a
unread,
BB5 arXiv release
Hello everyone, We've released the BB5 paper on arXiv: https://arxiv.org/pdf/2509.12337 Have a
Sep 17
Shawn Ligocki
Sep 4
TMBR: Aug 2025
TMBR (This Month in Beaver Research, "timber") Aug 2025 is now available: https://wiki.
unread,
TMBR: Aug 2025
TMBR (This Month in Beaver Research, "timber") Aug 2025 is now available: https://wiki.
Sep 4
Shawn Ligocki
Aug 10
TMBR: July 2025
I'm starting a new monthly article series, This Month in Beaver Research (TMBR, pronounced "
unread,
TMBR: July 2025
I'm starting a new monthly article series, This Month in Beaver Research (TMBR, pronounced "
Aug 10
Shawn Ligocki
,
Tristan Stérin
2
Jun 26
BB(6) > 2^^2^^2^^9
Note that the previous 10^^(10^7) champion has been verified in Coq (https://github.com/ccz181078/
unread,
BB(6) > 2^^2^^2^^9
Note that the previous 10^^(10^7) champion has been verified in Coq (https://github.com/ccz181078/
Jun 26
Shawn Ligocki
May 16
BB(7) > Ack(11)
Pavel found an Ackermann level BB(7) TM last weekend. I evaluate that it halts with a sigma score
unread,
BB(7) > Ack(11)
Pavel found an Ackermann level BB(7) TM last weekend. I evaluate that it halts with a sigma score
May 16
Shawn Ligocki
Apr 21
5% Chance of new BB(6) Champ
Racheline from bbchallenge Discord has discovered a TM which has a 5% chance to beat the current BB(6
unread,
5% Chance of new BB(6) Champ
Racheline from bbchallenge Discord has discovered a TM which has a 5% chance to beat the current BB(6
Apr 21
nichol...@gmail.com
,
Shawn Ligocki
4
Mar 19
BBB(3, 3) ≥ 10 ↑↑ 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^{
unread,
BBB(3, 3) ≥ 10 ↑↑ 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^{
Mar 19
Shawn Ligocki
Mar 3
BB(4,3) > 2↑↑↑(2^2^32)
The TM 0RB1RZ0RB_1RC1LB2LB_1LB2RD1LC_1RA2RC0LD was found by Pavel Kropitz back in May 2024 along with
unread,
BB(4,3) > 2↑↑↑(2^2^32)
The TM 0RB1RZ0RB_1RC1LB2LB_1LB2RD1LC_1RA2RC0LD was found by Pavel Kropitz back in May 2024 along with
Mar 3
Andrés Sancho
,
Shawn Ligocki
2
Feb 11
num(5) = 165
Great find Andrés! A couple notes: The terminology "num(5)" comes from (Ben-Amram AM,
unread,
num(5) = 165
Great find Andrés! A couple notes: The terminology "num(5)" comes from (Ben-Amram AM,
Feb 11
Ewan Donovan
,
Terry Ligocki
4
Feb 7
Question about BB(n) and different tape configurations.
You're very welcome. Hope to “see” you on the discord! Sent by modern magic - TJL On Feb 6, 2025,
unread,
Question about BB(n) and different tape configurations.
You're very welcome. Hope to “see” you on the discord! Sent by modern magic - TJL On Feb 6, 2025,
Feb 7
Daniel Yuan
, …
Pascal Michel
5
Jan 17
New 2-state 5-symbol champion!
(1) Erratum: the first overflow rule should be 0 (11)^(x + 2) <A (23)^(y + 2) 0^3 --( 4x + 8y + 53
unread,
New 2-state 5-symbol champion!
(1) Erratum: the first overflow rule should be 0 (11)^(x + 2) <A (23)^(y + 2) 0^3 --( 4x + 8y + 53
Jan 17
Nicholas Drozd
, …
Terry Ligocki
33
10/31/24
Lin recurrence periods
Hey, I'm really late to the party but it was great to see what you've been working on and
unread,
Lin recurrence periods
Hey, I'm really late to the party but it was great to see what you've been working on and
10/31/24
Shawn Ligocki
9/20/24
One Collatz Coincidence
It turns out that many TMs (including the BB(5) and BB(2,4) champions) all simulate equivalent
unread,
One Collatz Coincidence
It turns out that many TMs (including the BB(5) and BB(2,4) champions) all simulate equivalent
9/20/24
Shawn Ligocki
, …
Pascal Michel
8
9/5/24
BB(3, 4) > Ack(14)
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
unread,
BB(3, 4) > Ack(14)
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
9/5/24
Shawn Ligocki
8/27/24
BB(2,4) proven
@mxdys has adapted their BB(5) Coq proof to show that S(2,4) = 3932964: https://www.sligocki.com/2024
unread,
BB(2,4) proven
@mxdys has adapted their BB(5) Coq proof to show that S(2,4) = 3932964: https://www.sligocki.com/2024
8/27/24
Shawn Ligocki
2
7/2/24
BB(5) Proven in Coq
Also, Blog post by Scott Aaronson about the new result: https://scottaaronson.blog/?p=8088 HackerNews
unread,
BB(5) Proven in Coq
Also, Blog post by Scott Aaronson about the new result: https://scottaaronson.blog/?p=8088 HackerNews
7/2/24
Shawn Ligocki
, …
Terry Ligocki
4
5/30/24
Allen Brady's Obituary
"I'm saddened by this..." On Wed, May 29, 2024 at 2:36 PM Terry Ligocki <tjligocki@
unread,
Allen Brady's Obituary
"I'm saddened by this..." On Wed, May 29, 2024 at 2:36 PM Terry Ligocki <tjligocki@
5/30/24
Pascal Michel
,
uni...@fu-solution.com
2
5/14/24
A (4,3) TM that never halts
sorry for the wasted effort. i've brushed up the code and fixed the bug and the good news is that
unread,
A (4,3) TM that never halts
sorry for the wasted effort. i've brushed up the code and fixed the bug and the good news is that
5/14/24
Shawn Ligocki
2
11/30/23
Spam
Ug, the spammers joined the group! I have added more restrictions including users having to request
unread,
Spam
Ug, the spammers joined the group! I have added more restrictions including users having to request
11/30/23
Shawn Ligocki
, …
Pascal Michel
4
11/9/23
BB(3, 3) is Hard
I give here more analysis of this (3,3) machine. If A(a,b,c) = ...0(12)^a (11)^b < A (11)^c 0...,
unread,
BB(3, 3) is Hard
I give here more analysis of this (3,3) machine. If A(a,b,c) = ...0(12)^a (11)^b < A (11)^c 0...,
11/9/23
Shawn Ligocki
10/19/23
Green's Machines
I have often heard about Milton Green's 1964 TMs, but found it hard to understand their behavior
unread,
Green's Machines
I have often heard about Milton Green's 1964 TMs, but found it hard to understand their behavior
10/19/23
uni...@fu-solution.com
, …
Shawn Ligocki
8
9/22/23
BB(2, 5) > 7.3 x 10^19016
Pascal, you inspired me to dig a little more into this TM! I also found it hard to characterize the
unread,
BB(2, 5) > 7.3 x 10^19016
Pascal, you inspired me to dig a little more into this TM! I also found it hard to characterize the
9/22/23
Shawn Ligocki
, …
nichol...@gmail.com
10
9/1/23
BB(2, 6) > 10↑↑70
I am delighted to report that my simulator is now able to verify Shawn's 10^^70 TM. The other big
unread,
BB(2, 6) > 10↑↑70
I am delighted to report that my simulator is now able to verify Shawn's 10^^70 TM. The other big
9/1/23
Pascal Michel
7/17/23
My webpages
My webpages about busy beavers are no longer at https://webusers.imj-prg.fr/~pascal.michel/index.html
unread,
My webpages
My webpages about busy beavers are no longer at https://webusers.imj-prg.fr/~pascal.michel/index.html
7/17/23
Shawn Ligocki
, …
Pascal Michel
5
6/2/23
BB(2, 6) > 10↑↑10↑↑10↑↑3
I give here more analyses on the Turing machine p3 found by Pavel Kropitz on May 19, 2023, with s(p3)
unread,
BB(2, 6) > 10↑↑10↑↑10↑↑3
I give here more analyses on the Turing machine p3 found by Pavel Kropitz on May 19, 2023, with s(p3)
6/2/23
Shawn Ligocki
5/17/23
BB(3, 4) > 10↑↑2048
Pavel Kropitz found a 3-state, 4-symbol TM which scores > 10↑↑2048! He originally shared it on the
unread,
BB(3, 4) > 10↑↑2048
Pavel Kropitz found a 3-state, 4-symbol TM which scores > 10↑↑2048! He originally shared it on the
5/17/23
Heiner Marxen
,
Shawn Ligocki
2
5/3/23
An encoding of large numbers
Thanks Heiner, this is very interesting. I especially like how they have made a standard way to
unread,
An encoding of large numbers
Thanks Heiner, this is very interesting. I especially like how they have made a standard way to
5/3/23
Pascal Michel
, …
Terry Ligocki
4
4/13/23
Paper from Vielhaber et al. on arxiv
Also, we may only be finding Collatz-like behavior in the BB candidates because it is one of the more
unread,
Paper from Vielhaber et al. on arxiv
Also, we may only be finding Collatz-like behavior in the BB candidates because it is one of the more
4/13/23
Konkhra
, …
Shawn Ligocki
3
11/24/22
AlphaTensor
Long ago when I started looking for Busy Beavers, my Dad and I tried using Simulated Annealing: https
unread,
AlphaTensor
Long ago when I started looking for Busy Beavers, my Dad and I tried using Simulated Annealing: https
11/24/22