Chasing the Longest-Running Simple Computer Program

The article discusses the ongoing challenge in theoretical computer science to determine the values of busy beaver numbers, which grow unimaginably large and are linked to the halting problem. Recent discoveries have pushed the known lower bounds for BB(6) to extraordinary levels, involving operations like tetration and pentation, highlighting the complexity and the collaborative efforts in this field. The quest continues, with some problems related to busy beaver machines connected to unsolved mathematical conjectures.