Famously, Oppenheimer and co worked out how close a nuclear bomb test would be to causing a chain reaction of nitrogen fusion in the atmosphere. They made a lot of worst-case-scenario assumptions and still came to the conclusion that no, a nuclear bomb test wouldn’t scour the surface of the world.
But let’s say the atmosphere was twice as dense as it is. Or ten times as dense. At what point would that calculation turn very, very scary?
Edit: man, seriously, most of the people ‘answering’ this question didn’t even read it.
Yeah, you’re not going to get a self-sustaining reaction in Earth’s atmosphere if it wasn’t already hot and compressed enough that there would be a self-sustaining reaction happening anyway. It’s just not a plausible concern. You only get self-sustaining fusion in stars, so Earth would have to be a star in this scenario.