BB(7)
The 7-state, 2-symbol Busy Beaver problem, BB(7), refers to the unsolved 7th value of the Busy Beaver function. With the compilation of the Cryptid machine Bigfoot into a 7-state, 2-symbol machine in May 2024, we now know that we must solve a Collatz-like problem in order to solve BB(7).
The current BB(7) champion 1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF (bbch) was discovered by Pavel Kropitz in May 2025, proving the lower bound:
History
Before 2025, the only known BB(7) champions were produced by hand, not by search. In 1964, Milton Green designed a machine that had sigma score 22,961. In 2014, Wythagoras modified a BB(6) champion to produce a machine that had sigma score .
In May 2025, mxdys shared C++ code that breaks up the BB(7) enumeration into 1 million subtasks which each run for about 2 minutes and leave ~100 holdouts each. Various folks on Discord have been investigating different sections of this domain to search for champions.
Within three days of the code's release, the Ligockis found three champions after applying their deciders to enumerator output. Shawn Ligocki found the first two, 1RB0RF_1LC0RE_1RD1LB_1LA1LD_0RA0LE_1RG0LB_1RZ1RB (bbch) and 1RB1RA_1RC0LC_0LD1LG_1LF0LE_1RZ1LF_0LA1LD_1RA1LC (bbch), with sigma scores of approximately 10 ↑↑ 22 and 10 ↑↑ 35. That evening, Terry Ligocki found 1RB0LG_1RC0RF_1LD1RZ_1LF0LE_1RA1LD_1LG1RE_0LB0LB (bbch), with sigma score ~10 ↑↑ 46. A few days later, Pavel found a TM that outpaces all of them.
Pavel's champion is enumerated in subtask 243308.
Top Halters
Based on limited search through a subset of the 1 million subtasks from mxdys's code, the top 20 scoring known machines are:
| TM | Approximate sigma score | Discoverer |
|---|---|---|
1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF (bbch)
|
Pavel Kropitz | |
1RB1RZ_0RC0RE_1LD1LA_1LC0LG_0RF1LF_0RD1LF_1LB0LE (bbch)
|
10 ↑↑ 519.20 | Andrew Ducharme |
1RB1RZ_0RC0RE_1LD1LA_1LC0LG_0RF1LE_0RD1LF_1LB0LE (bbch)
|
10 ↑↑ 519.20 | Andrew Ducharme |
1RB1RZ_0RC0RE_1LD1LA_1LC0LG_0RF1LE_0RD0LG_1LB0LE (bbch)
|
10 ↑↑ 519.20 | @gerbil5709, Terry Ligocki |
1RB1RF_0RC1RG_1LD1LE_0LE1LD_0RF0LC_1RA0LC_0RF1RZ (bbch)
|
10 ↑↑ 286.17 | Terry Ligocki |
1RB0LE_1RC0RA_1RD0RC_1LE1LD_1LA0LF_0LA0LG_1RZ0RD (bbch)
|
10 ↑↑ 246.32 | @Iijil |
1RB0LE_1RC0RA_1RD0RC_1LE1LD_1LA0LF_0LA1LG_1RZ1LA (bbch)
|
10 ↑↑ 246.32 | @star, Terry Ligocki |
1RB1RZ_1RC0LE_0RD1RB_1LE1RA_1LF0LG_0LG0RG_1LB1RG (bbch)
|
10 ↑↑ 243.88 | @Iijil, Andrew Ducharme |
1RB0RB_1LC1RG_1RD1RC_1RE0RA_1LF0LB_1RF0LE_0RD1RZ (bbch)
|
10 ↑↑ 228.78 | Terry Ligocki |
1RB0LD_0LC1RZ_1RA0RD_1RE1LD_1LF0RC_0LG1LE_1RG0LD (bbch)
|
10 ↑↑ 192.67 | Terry Ligocki |
1RB1LA_1LC0RE_0LD1LB_1RD0LA_1RF0RA_0RG0LA_1RB1RZ (bbch)
|
10 ↑↑ 192.67 | Terry Ligocki |
1RB1LA_1LC0RE_0LD1LB_1RD0LA_1RF0RA_1RG0LA_0LE1RZ (bbch)
|
10 ↑↑ 192.67 | Terry Ligocki |
1RB1RZ_1LC0RE_0LD1LB_1RE0LA_1RF0RG_0RA0LG_1RB1LG (bbch)
|
10 ↑↑ 192.67 | Terry Ligocki |
1RB1RZ_1LC0RE_0LD1LB_1RE0LA_1RF0RG_0RG0LG_1RB1LG (bbch)
|
10 ↑↑ 192.67 | Terry Ligocki |
1RB1RZ_1LC0RE_0LD1LB_1RE0LG_1RF0RG_0RA0LG_1RB1LG (bbch)
|
10 ↑↑ 192.67 | Terry Ligocki |
1RB0LD_0LC1RZ_1RA0RD_1RE1LD_1LF0RC_0LG1LE_1RC0LD (bbch)
|
10 ↑↑ 192.67 | Andrew Ducharme |
1RB1LA_1LC0RE_0LD1LB_1RE1LG_1RF0LG_0RA0LA_0RF1RZ (bbch)
|
10 ↑↑ 192.67 | Andrew Ducharme |
1RB1LA_1LC0RF_0LD0RD_1RF1LE_1LB1RZ_1RG0RA_0RA0LA (bbch)
|
10 ↑↑ 192.67 | @C7X |
1RB1LA_1LC0RE_0LD1LB_1RE0LA_1RF0RA_0RG0LA_1RB1RZ (bbch)
|
10 ↑↑ 192.67 | @Iijil, Terry Ligocki |
1RB1LA_1LC0RE_0LD1LB_1RE0LA_1RF0RA_1RG0LA_0LE1RZ (bbch)
|
10 ↑↑ 192.67 | @Iijil, Terry Ligocki |
The top 20 known halters with unique scores are:
| TM | Approximate sigma score | Discoverer |
|---|---|---|
1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF (bbch)
|
Pavel Kropitz | |
1RB1RZ_0RC0RE_1LD1LA_1LC0LG_0RF1LF_0RD1LF_1LB0LE (bbch)
|
10 ↑↑ 519.20 | Andrew Ducharme |
1RB1RF_0RC1RG_1LD1LE_0LE1LD_0RF0LC_1RA0LC_0RF1RZ (bbch)
|
10 ↑↑ 286.17 | Terry Ligocki |
1RB0LE_1RC0RA_1RD0RC_1LE1LD_1LA0LF_0LA0LG_1RZ0RD (bbch)
|
10 ↑↑ 246.32 | @Iijil |
1RB1RZ_1RC0LE_0RD1RB_1LE1RA_1LF0LG_0LG0RG_1LB1RG (bbch)
|
10 ↑↑ 243.88 | @Iijil, Andrew Ducharme |
1RB0RB_1LC1RG_1RD1RC_1RE0RA_1LF0LB_1RF0LE_0RD1RZ (bbch)
|
10 ↑↑ 228.78 | Terry Ligocki |
1RB1RZ_1LC0RE_0LD1LB_1RE0LA_1RF0RG_0RA0LG_1RB1LG (bbch)
|
10 ↑↑ 192.67 | Terry Ligocki |
1RB0LC_1LC1LD_1LA1LB_0LG1RE_1LD0RF_0RA1RE_1RZ1LA (bbch)
|
10 ↑↑ 188.28 | Terry Ligocki |
1RB0LC_1LC0LD_1LA1LB_0LG1RE_1LD0RF_0RA1RE_1RZ1LC (bbch)
|
10 ↑↑ 140.28 | @stokastic |
1RB0RF_1RC1RZ_0LD1RF_0RA1LE_0LC1LF_1LE0RG_0LE1RA (bbch)
|
10 ↑↑ 136.64 | Katelyn Doucette, Andrew Ducharme |
1RB0LG_0RC1RZ_1LD0LA_1RE1LE_1LC1RF_0RE0RA_0RF1LG (bbch)
|
10 ↑↑ 133.85 | @poppuncher |
1RB1RZ_1RC0RF_1LD1RB_1RG0LE_1LD0RA_1RE0LD_0RC1LF (bbch)
|
10 ↑↑ 129.24 | @Iijil |
1RB0LC_1RC0RG_1RD0LF_1RE0RF_1LA1RG_1LE1LF_1RZ1RD (bbch)
|
10 ↑↑ 126.20 | @stokastic |
1RB0LD_1RC1RA_0RD1RG_1LE1LF_0LF1LE_0RA0LD_0RA1RZ (bbch)
|
10 ↑↑ 124.86 | Terry Ligocki |
1RB1LF_1RC1RA_1LD0LD_1LA1LE_0LA0LD_1LG0RF_0LE1RZ (bbch)
|
10 ↑↑ 116.98 | Terry Ligocki |
1RB0RD_1RC0LA_0LA0LE_1RE1RZ_1RF0RA_1LG0LE_1LC0LG (bbch)
|
10 ↑↑ 116.05 | |
1RB0RD_1RC0RA_0RD1LD_0LE1LF_1LA0LG_0LC1LB_1LC1RZ (bbch)
|
10 ↑↑ 115.52 | @prurq |
1RB0RG_1LC0LE_1LD0LB_0LE1RE_0RA1RF_0RD1RC_1RD1RZ (bbch)
|
10 ↑↑ 114.83 | Andrew Ducharme |
1RB0RE_1LC0LA_1LD0LC_0LE0LA_1RF0RG_1RD0LE_1RA1RZ (bbch)
|
10 ↑↑ 114.60 | Shawn Ligocki |
1RB0RE_0RC1LC_0LD1LF_1LE0LG_1RA0RC_0LB1LA_1LB1RZ (bbch)
|
10 ↑↑ 114.57 | Andrew Ducharme |
Summary of Phase 1
Phase 1's first two stages were carried out from May 2025 to July 2025. The table below summaries some of that activity and was used to coordinate the effort of doing the raw computation. Fourteen people (see below) contributed directly and the overall bbchallenge group participated in discord discussions, etc.
Stage 1, "enumeration" in the table, involved running 1 million subtasks using mxdy's code in 100 batches of 10 thousand subtasks.
Stage 2, "linear rule" in the table, processing the output of Stage 1 using Shawn Ligocki's linear rule code which also used a few other deciders, e.g., a version of CTL.
Stage 3, the final stage of Phase 1, is the compilation, verification, and presentation of the final results from Phase 1. It is ongoing but should be completed during August 2025.
| Task range | Done by | Completed | # holdouts | Maximum Score TM | ~Sigma | Source | |
|---|---|---|---|---|---|---|---|
| enumeration | linear rule | ||||||
| 00-01xxxx | @Iijil | Yes | Yes | 1,545,673 | 1RB0LE_1RC0RA_1RD0RC_1LE1LD_1LA0LF_0LA0LG_1RZ0RD (bbch)
|
10 ↑↑ 246.32 | Google Drive folder |
| 02-04xxxx |
@Iijil |
Yes | Yes | 2,279,734 | 1RB0LF_1RC1RA_1RD0RG_1LE1RZ_1LA0LF_1RA1LE_0RE1RG (bbch)
|
10 ↑↑ 93.81 | |
| 05-09xxxx |
@Iijil |
Yes | Yes | 3,889,955 | 1RB1RZ_1RC0LE_0RD1RB_1LE1RA_1LF0LG_0LG0RG_1LB1RG (bbch)
|
10 ↑↑ 243.88 | |
| 10-12xxxx | Andrew Ducharme | Yes | Yes | 2,708,888 | 1RB1RZ_0RC0RE_1LD1LA_1LC0LG_0RF1LE_0RD1LF_1LB0LE (bbch)
|
10 ↑↑ 519.20 | Google Drive folder |
| 13xxxx | Shawn Ligocki | Yes | Yes | 1,192,442 | 1RB0RE_1LC0LA_1LD0LC_0LE0LA_1RF0RG_1RD0LE_1RA1RZ (bbch)
|
10 ↑↑ 114.60 | Google Drive folder |
| 14-16xxxx | Andrew Ducharme | Yes | Yes | 2,701,637 | 1RB0LC_1LC1LD_1LA1LB_0LG1RE_0RF0LD_0RA1RE_1RZ1LA (bbch)
|
10 ↑↑ 188.28 | Google Drive folder |
| 17-18xxxx |
@gerbil5709 |
Yes | Yes | 1,898,156 | 1RB1LA_1LC0RE_0LD1LB_1RE0LA_1RF0RA_0RG0LA_1RB1RZ (bbch)
|
10 ↑↑ 192.67 | |
| 19xxxx |
Katelyn Doucette |
Yes | Yes | 1,099,752 | 1RB0RF_1RC1RZ_0LD1RF_0RA1LE_0LC1LF_1LE0RG_0LE1RA (bbch)
|
10 ↑↑ 136.64 | Google Drive folder |
| 20-23xxxx | @C7X | Yes | Yes | 4,528,827 | 1RB1LA_1LC0RF_0LD0RD_1RF1LE_1LB1RZ_1RG0RA_0RA0LA (bbch)
|
10 ↑↑ 192.67 | Google Drive folder |
| 24xxxx | Andrew Ducharme | Yes | Yes | 712,356 | 1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF (bbch)*
|
Google Drive folder | |
| 25-34xxxx | @stokastic | Yes | Yes | 10,339,816 | 1RB0LC_1LC0LD_1LA1LB_0LG1RE_1LD0RF_0RA1RE_1RZ1LC (bbch)
|
10 ↑↑ 140.28 | Google Drive folder |
| 35-39xxxx | Terry Ligocki | Yes | Yes | 4,894,047 | 1RB1RZ_1LC0RF_0LD1LB_1RD0LE_1RB1LE_1RG0RE_0RA0LE (bbch)
|
10 ↑↑ 192.67 | Google Drive folder |
| 40-47xxxx | Andrew Ducharme | Yes | Yes | 6,181,327 | 1RB1RZ_0RC0RE_1LD1LA_1LC0LG_0RF1LF_0RD1LF_1LB0LE (bbch)
|
10 ↑↑ 519.20 | Google Drive folder |
| 48xxxx |
@star |
Yes | Yes | 727,875 | 1RB0LE_1RC0RA_1RD0RC_1LE1LD_1LA0LF_0LA1LG_1RZ1LA (bbch)
|
10 ↑↑ 246.32 | |
| 49xxxx |
Tobiáš Brichta |
Yes | Yes | 804,722 | 1RB0LG_1RC0RG_0LD1RE_1RD0RE_1LF1RB_0LA1RZ_1LC1LG (bbch)
|
10 ↑↑ 126.20 | |
| 50xxxx |
@prurq |
Yes | Yes | 797,224 | 1RB0RD_1RC0RA_0RD1LD_0LE1LF_1LA0LG_0LC1LB_1LC1RZ (bbch)
|
10 ↑↑ 115.52 | Google Drive folder |
| 51-53xxxx |
@gerbil5709 |
Yes | Yes | 3,016,175 | 1RB0LC_1LC0LD_1LA1LB_0LG1RE_0RF0RF_0RA1RE_1RZ1LC (bbch)
|
10 ↑↑ 140.28 | |
| 54-59xxxx | Terry Ligocki | Yes | Yes | 5,689,850 | 1RB0LC_1LC1LD_1LA1LB_0LG1RE_0RF0RF_0RA1RE_1RZ1LA (bbch)
|
10 ↑↑ 188.28 | Google Drive folder |
| 60-64xxxx |
@gerbil5709 |
Yes | Yes | 3,817,876 | 1RB1RZ_0RC0RE_1LD1LA_1LC0LG_0RF1LE_0RD0LG_1LB0LE (bbch)
|
10 ↑↑ 519.20 | |
| 65-68xxxx | Terry Ligocki | Yes | Yes | 3,076,778 | 1RB0LD_0LC1RZ_1RA0RD_1RE1LD_1LF0RC_0LG1LE_1RG0LD (bbch)
|
10 ↑↑ 192.67 | Google Drive folder |
| 69xxxx | @poppuncher | Yes | Yes | 1,053,119 | 1RB0LG_0RC1RZ_1LD0LA_1RE1LE_1LC1RF_0RE0RA_0RF1LG (bbch)
|
10 ↑↑ 133.85 | Google Drive folder |
| 70-71xxxx | @hipparcos | Yes | Yes | 1,899,094 | 1RB1RZ_1LC1RD_0LD0LC_1LE1RA_1LF0LE_1RF0RG_1RG0RD (bbch)
|
10 ↑↑ 77.50 | Github release |
| 72-79xxxx | Terry Ligocki | Yes | Yes | 7,627,514 | 1RB0RB_1LC1RG_1RD1RC_1RE0RA_1LF0LB_1RF0LE_0RD1RZ (bbch)
|
10 ↑↑ 228.78 | Google Drive folder |
| 80-81xxxx | @xnoobspeakable | Yes | Yes | 1,537,533 | 1RB0LA_0RC1RZ_0RD0RG_1LE1RA_1LF1LD_1RG0RG_1RD1RC (bbch)
|
10 ↑↑ 74.85 | Google Drive folder |
| 82-99xxxx | Terry Ligocki | Yes | Yes | 15,673,786 | 1RB1RF_0RC1RG_1LD1LE_0LE1LD_0RF0LC_1RA0LC_0RF1RZ (bbch)
|
10 ↑↑ 286.17 | Google Drive folder |
*The current BB(7) champion TM 1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF (bbch)* was discovered by Pavel Kropitz in the enumeration of subtask 243308. The remaining subtasks in the 24xxxx range were enumerated and filtered by Andrew Ducharme.
Exploration after Phase 1
People are now looking at reducing the number of holdouts, ~85M TMs, after Phase 1. They are trying different deciders not used in Phase 1 and different parameters with the deciders used in Phase 1. This table is somewhere they can put the results of these explorations so there is a record of what is being done. It is hoped this will inspire everyone to contribute when they can, a reference point for discord discussions, and something that can be questioned and/or verified.
| Done by | Input TMs | Output TMs | % reduction | Description | Source |
|---|---|---|---|---|---|
| Your name/id here | 1,500,000 | 900,000 | 40% | Somewhere on the interweb | |
| Shawn Ligocki | 858,538 | 733,830 | 14.5% | Translated Cycler and CPS on 7x2_p01_s02_holdouts_rand_13.txt
|
Discord link |