# BusyBeaver(5) is 47,176,870

last updated: Jul 08, 2024

Only now, after an additional 41 years, do we know the fifth Busy Beaver value... BB(5) is equal to 47,176,870—the value that’s been conjectured since 1990, when Heiner Marxen and Jürgen 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 forever—or in other words, that 47,176,870 is the maximum finite number of steps for which any 5-state Turing machine can run. That’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:

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

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