"Imagine that someone gives you a list of five numbers: 1, 6, 21, 107 and-wait for it-47,176,870. Can you guess what comes next? If you're stumped, you're not alone. These are the first five busy beaver numbers. They form a sequence that's intimately tied to one of the most notoriously difficult questions in theoretical computer science. Determining the values of busy beaver numbers is a daunting challenge that has attracted a cult following among both professional and amateur mathematicians for over 60 years."
"Researchers identified the first four busy beaver numbers in the 1960s and 1970s. The conspicuously larger fifth number, called BB(5), was only definitively pinned down last year, by a team made up mostly of amateur mathematicians working together in an online community called the Busy Beaver Challenge. No one knows how big BB(6) is. All we have are lower limits-truly staggering ones. In 2022 busy beaver hunters established that BB(6) must be, at a minimum, so large that it's literally impossible to write down in ordinary decimal notation."
The Busy Beaver sequence begins 1, 6, 21, 107, 47,176,870. The sequence connects to a notorious question in theoretical computer science about maximal outputs of Turing machines. Researchers found the first four busy beaver numbers in the 1960s and 1970s. BB(5) was definitively determined by a largely amateur team collaborating in an online community called the Busy Beaver Challenge. BB(6) remains unknown; only lower bounds exist. In 2022 hunters proved that BB(6) exceeds the capacity to be written in ordinary decimal notation, even if digits were carved into every atom in the universe. Recent work produced even larger lower bounds within days.
Read at WIRED
Unable to calculate read time
Collection
[
|
...
]