# BusyBeaver(5) is 47,176,870

*last updated: Jul 08, 2024*

Only now, after an additional 41 years, do we know the

fifthBusy Beaver value... BB(5) is equal to 47,176,870â€”the value thatâ€™s beenconjecturedsince 1990, when Heiner Marxen and JÃ¼rgen Buntrock discovered a 5-state Turing machine that runs for exactly 47,176,870 steps before halting, when started on a blank tape. The new bbchallenge achievement is to prove that all 5-state Turing machines that run for more steps than 47,176,870, actually run foreverâ€”or in other words, that 47,176,870 is the maximumfinitenumber of steps for which any 5-state Turing machine can run. Thatâ€™s what it means for BB(5) to equal 47,176,870.

I like to follow along with computer science achievements when I can, and this one is super easy to state in the abstract: BB(5) is the maximum number of steps a 5 state Turing machine with two symbols can run, and still halt.

The details of course, are more challenging, and Scott's article does a great job sketching out some of them.

One fun note he mentions is that BB(6) is known to be at least 10 raised to itself 15 times, the wonderful number:

$10^{10^{10^{10^{10^{10^{10^{10^{10^{10^{10^{10^{10^{10^{10}}}}}}}}}}}}}}$

Scott links a few other sources:

- Quanta
- bbchallenge (the online organization that coordinated the effort)

It is very cool that the team used Coq to prove the theorem in an executable format.