BusyBeaver(5) is now known to be 47,176,870
The Busy Beaver function's fifth value, BB(5), is 47,176,870, confirmed by the bbchallenge collaboration using the Coq proof system after 41 years. This achievement highlights the function's complexity and human ingenuity.
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The Busy Beaver function's fifth value, BB(5), has been officially determined to be 47,176,870 after 41 years of speculation. This achievement was made by an international collaboration called bbchallenge, which used the Coq proof system to verify the result. The function represents the maximum finite number of steps a 5-state Turing machine can run before halting. The collaboration's success in proving all 5-state Turing machines that run for more steps than 47,176,870 run forever showcases the function's complexity. The process involved meticulous verification of non-halting proofs and organizing efforts through online platforms. The significance of determining Busy Beaver numbers lies in measuring human progress against the vastness of mathematical possibilities, akin to space exploration milestones. The discovery of BB(5) stands as a testament to human ingenuity amidst challenging times.
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David Turner explores optimizing leap year calculations for performance gains by using bitwise operations and integer bounds. He presents efficient methods, mathematical proofs, and considerations for signed integers, highlighting limitations pre-Gregorian calendar.
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