The busy beaver function (a.k.a. BB function or Radó's sigma function, denoted \(\Sigma(n)\) or \( ext{BB}(n)\)), is a distinctive fast-growing function from computability theory. It is notable as being the most well-known of the uncomputable functions. It is defined as the maximum number of ones that can be written (in the finished tape) with an n-state, 2-color halting Turing machine starting from a blank tape before halting.