In theoretical computer science, the busy beaver game aims at finding a terminating program of a given size that (depending on definition) either produces the most output possible, or runs for the longest number of steps.
Busy beaver - wiki
The Busy Beaver Frontier
Busy beavers and Kolmogorov complexity
Problems in number theory from busy beaver competition
On Logical Depth and the Running Time of Shortest Programs
The “paradox” of computability and a recursive relative version of the busy beaver function
Relativizing an incompressible number and an incompressible function through subrecursive extensions of Turing machines
The Busy Beaver Competition: a historical survey
Busy beavers gone wild
Bounds on the rates of growth and convergence of all physical processes
Friedman’s “Long Finite Sequences”: The End of the Busy Beaver Contest
Turing Completeness and Sid Meier’s Civilization