BB(2,7)

The 2-state, 7-symbol Busy Beaver problem, BB(2,7), is unsolved. With Cryptids like Hydra in the preceding domain BB(2,5), we know that we must solve a Collatz-like problem in order to solve BB(2,7). The current BB(2,7) champion is simply inherited from BB(2,6) as BB(2,7) is just starting to be explored.

Top Halters

These are the 20 highest scoring machines that were found in the current investigation of BB(2,7). This list does not include TMs from smaller domains:

Phase 1

The initial phase of enumeration and reduction of holdouts started in November 2025 using C++ code mxdys shared. This work is ongoing and further described below. After this is completed, it is planned to run the Ligockis' Enumerate.py code to further reduce the number of holdout TMs.

Stage 1

The code provided by mxdys breaks up the BB(2,7) enumeration into 1 million subtasks which each run for ~10 minutes and leave ~2500 holdouts based on an average of the first 1K subtasks. These values are about 5 times longer than and 25 times larger than the ones for BB(7).

This enumeration began in November 2025 and is summarized in the table below. The mxdys code main.cpp from C++ code was used with two modification: #define BB7 was replaced with #define BB27 and the following block of code was added in the section with BB domain definitions:

#ifdef BB27
constexpr int64_t N_STATE=2;
constexpr int64_t N_CHAR=7;
constexpr int64_t log2_N_STATE=1;
constexpr int64_t log2_N_CHAR=3;
typedef uint8_t chr_t;
#endif

Results:

Task range	Done by	Completed	# holdouts	Source
00-09xxxx	Terry Ligocki	Yes	309,868,865	Google Drive
10-19xxxx		Yes	315,243,072
20-29xxxx		Yes	309,968,380
30-39xxxx		Yes	315,040,474
40-49xxxx		Yes	309,976,212
50-59xxxx		Yes	314,996,395
60-69xxxx		Yes	309,917,121
70-79xxxx		Yes	315,355,885
80xxxx		Yes	26,686,275
81xxxx		Yes	35,313,171
82xxxx		Yes	26,627,542
83xxxx		No	TBD
84xxxx		Yes	26,666,095
85xxxx		No	TBD
86xxxx		No	TBD
87-99xxxx	TBD	No	TBD	---
Cumulative	---	---	2,615,659,487	---

Stage 2

The Ligocki's "Enumerate.py" Python code is used to further reduce the number of holdouts and explore more of the TNF of BB(2,7).