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
00xxxx	Terry Ligocki	Yes	26,731,369	Google Drive
01xxxx		Yes	35,330,915
02xxxx		Yes	26,668,256
03xxxx		Yes	35,295,006
04xxxx		Yes	26,636,460
05xxxx		Yes	35,307,052
06xxxx		Yes	26,624,351
07xxxx		Yes	35,325,910
08xxxx		Yes	26,703,864
09xxxx		No	TBD	---
10-99xxxx	TBD	No	TBD	---
Cumulative	---	---	274,623,183	---

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).