TMBR: September 2025

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This Month in Beaver Research for September 2025.

TODO: BB(5) arXiv released https://arxiv.org/abs/2509.12337

TODO: BB(3,3) month.

In the News

14 Sep 2025. Ben Brubaker. Wired. The Quest to Find the Longest-Running Simple Computer Program.
17 Sep 2025. Hacker News. Determination of the fifth Busy Beaver value.
18 Sep 2025. Tuomas Kangasniemi. Tekniikkatalous. Iso matematiikan ongelma ratkesi 63 v jälkeen (Finnish) (English: A big math problem solved after 63 years).

Holdouts

BB(6):
- Andrew Ducharme and @mxdys both found a family of 10 halting TMs independently, all halting in around $10^{69}$ steps.
- @mxdys decided two machines’ fates from the 50 Random Holdouts released in August, making 8/50 machined solved as of this month.
- Andrew Ducharme found a non-halting TM, to which Peacemaker II replied with another machine that turned out to be very similar, and non-halting as well. Later in his search Andrew found another non-halting TM.
- TODO: mxdys decided 776 holdouts using a new equivalence
BB(7):
- Andrew Ducharme has continued reducing the number of holdouts, from 59,727,905 to 28,189,617 (52.80% reduction)
- TODO: Terry Ligocki is running an additional 41 filters/parameters. 15 filters have been completed which reduced the holdouts from 28.2M to 24.9M (11.64% reduction).
BB(2,6):
- Andrew Ducharme has continued reducing the number of holdouts from 18,054,938 to 17,629,828 (2.35% reduction).
- Terry Ligocki shared that he ran 14 of @mxdys deciders on the holdouts list, reducing the holdout count to a flattering 1,300,334 TMs (92.63% reduction).
- @Peacemaker II discovered there were TMs missing from Andrew Ducharme's initial reductions. Andrew decided to scrap those reductions and run a single filter and reduced the holdout TMs from 22.3M to 20.4M (8.52% reduction).
- Terry Ligocki then reran the 14 filters on the corrected holdouts and reduced the holdouts from 20.4M to 1.43M (92.9% reduction). This was followed by running 36 filters found examining a subset of the holdouts which reduced the holdouts from 1.43M to 970K (32.2% reduction). Overall the 50 filters reduced the holdouts by 95.23%.
- TODO: Andrew Ducharme is continuing to run filters and has gotten some more appreciable reductions.
BB(4,3):
- TODO: Terry Ligocki is running a set of deciders/parameters from @mxdys' code to reduce the number of holdouts which are currently at ~461M TMs. Three passes have reduced the holdout count to ~96.7M TMs (an ~80% reduction).
BB(3,4):
- TODO: @Xnoob545 and @Lúkos are working on the holdout list for BB(3,4), ~435M TMs, using @mxdys' deciders with various parameters.