TMBR: July 2025
The very first edition of This Month in Busy Beaver for July 2025.
Champions
- (Late June) mxdys found a pair of new BB(6) champions pushing it into the pentational values:
1RB1RA_1RC1RZ_1LD0RF_1RA0LE_0LD1RC_1RA0RE(bbch) (scoring over 2↑↑2↑↑2↑↑10) and1RB1LC_1LA1RE_0RD0LA_1RZ1LB_1LD0RF_0RD1RB(bbch) (scoring over 10↑↑11010000). - mxdys confirms dyuan's BB(2,5) champion
1RB3LA4RB0RB2LA_1LB2LA3LA1RA1RZ(bbch). [1]
Holdout
- mxdys announced that BB(6) is down to 2891 holdouts. [2]
- A large group effort has enumerated BB(7) and filtered it down to less than 100 million holdouts. [3]
BB Adjacent
- Reversible Turing Machine Busy Beaver values calculated up to BB(5).
- TODO: Terminating Turmites / Relative Move Turing Machines
- TODO: BB n-instruction https://oeis.org/A384629 https://oeis.org/A384766 https://discord.com/channels/960643023006490684/960643023530762341/1393697378657374290
In the News
- 1 July 2025. The Quanta Podcast. How Amateurs Solved a Major Computer Science Puzzle.
- 2 July 2025. Manon Bischoff. Spektrum. Wie der sechste Fleißige Biber die Mathematik an ihre Grenzen bringt.
- 7 July 2025. Karmela Padavic-Callaghan. New Scientist. Mathematicians are chasing a number that may reveal the edge of maths. (Paywalled)
- 11 July 2025. New Scientist podcast episode 311. Discusses mxdys's BB(6) pentation result "We’re brushing up against the edge of mathematics".
- 11 July 2025. Darren Orf. Popular Mechanics. Mathematicians Say There’s a Number So Big, It’s Literally the Edge of Human Knowledge.
Interesting TMs
1RB1LC_1LB0RA_0LD---_1LE0LA_0LF0RG_1LG0LG_0RB1RG(bbch): Tetrational Fractal1RB1RE_1LC0RA_0RF0LD_1LE1LC_1RA0RC_---0RB(bbch): Skeleton Finger1RB1RG_1LC1RA_0LD0LC_0RE0RB_1RE1RF_1LD0LC_0LE---(bbch): Bouncer that transitions into a Counter1RB1RE_0RC1RG_1LD0LA_0LE0LF_0RA1RC_1LC0LE_---1RE(bbch): Counter that transitions into a Bouncer1RB2LA2LC---_1LA2RB2RD---_3RB1LC1RD0LA_3LA1RD1LC0RB(bbch): Sneaky almost-Cryptid