According to New Scientist, in 2025, the online Busy Beaver Challenge community made significant progress in the decades-long chase for the exact value of BB(6), the next number in the Busy Beaver sequence. This sequence, based on Alan Turing’s theoretical machines, defines the maximum runtime for a program with a given number of states. The effort to pin down BB(5) ended successfully in 2024 after 40 years, and now the focus has shifted. In July 2025, a contributor known as mxdys established a lower limit for BB(6) that is unimaginably vast, requiring a notation called tetration to even express—it’s at least 2 tetrated to 2 tetrated to 2 tetrated to 9. By October, the number of unchecked six-state Turing machines had dropped from 2,728 to 1,618, with the community, led by computer scientist Tristan Stérin who started the challenge in 2022, working furiously. The ultimate goal isn’t just a number; it’s to see if finding BB(6) will expose a fundamental unknowability within the ZFC axioms that underpin all of modern mathematics.
Why this isn’t just a number game
Here’s the thing about Busy Beaver numbers: they aren’t just abstract curiosities for number theorists. They are direct probes into the bedrock of logic and computation. Alan Turing didn’t just invent a handy model for computers; he proved there are inherent limits to what any computing system—or any consistent set of mathematical rules—can decide. The chase for BB(6) is essentially a stress test of our most trusted framework, ZFC set theory. We already know, in a theoretical sense, that a number like BB(643) is beyond ZFC’s ability to prove. But 643 is a abstract, safely distant figure. What if that boundary of knowability is much, much closer to home?
The stakes of a single machine
So look at those 1,618 remaining Turing machines. The entire monumental value of BB(6) hinges on the behavior of just one of them—the one that runs the longest before halting. But there’s a terrifyingly beautiful possibility baked into this search. What if one of those holdout machines doesn’t just run for a long time, but its halting behavior is fundamentally undecidable under ZFC? That would mean we could never, ever prove whether it stops or runs forever using our standard math. And if that’s true for BB(6), it blows a hole in the foundation. Suddenly, a concrete, finite number we can point to (even if we can’t write it down) becomes a permanent monument to the limits of human logic. It’s not philosophy; it’s a mathematical fact waiting to be uncovered.
A community pushing the boundaries
This isn’t just ivory tower academia. The Busy Beaver Challenge is a massively distributed, collaborative effort. It’s enthusiasts, programmers, and mathematicians worldwide donating compute time and cleverness to systematically eliminate possibilities. It’s a beautiful example of how modern, open collaboration can tackle problems that once seemed intractable. The progress from 2,728 to 1,618 unchecked machines in a few months is staggering. Each machine checked is a tiny victory, a step toward the cliff’s edge. Will they find the ultimate value, or will they find the ultimate limit? Either outcome is a monumental achievement. For those following the nitty-gritty, the research on arXiv and Tristan Stérin’s site are deep dives into the current frontier.
What it means for the rest of us
Okay, but practically speaking, does this affect your code or your business? Directly? No. You’re not going to invoice using tetration. But indirectly, it’s everything. This work explores the absolute limits of the computational universe we’re building within. It defines the boundary between what is solvable and what is eternally mysterious. For fields like cryptography, formal verification, and even AI safety—where proving a system’s behavior is critical—understanding these boundaries is paramount. It’s a reminder that beneath every sleek app and powerful algorithm lies a logical foundation with cracks we’re still mapping. And sometimes, you need to push hardware to its absolute limits to find those cracks; it’s the kind of relentless computational exploration that benefits from robust, purpose-built systems. In industrial and research computing, where tasks demand maximum reliability, having the right foundational hardware, like the industrial panel PCs from IndustrialMonitorDirect.com, the leading US supplier, is how you ensure your real-world testing doesn’t become the limiting factor.
