Dude is this 1940 ..really atmosohereic ignition ?
The thing is there's is almost no fuel to sustain even a traditional ignition reaction in the atmosphere , let alone nuclear , unless you want to imagine a bomb larger in force than any comet strike the planet has had in the major exstinctions we know of.
We have had comet strikes ( recently in geological terms) that have more tons of TNT than every nuke combined on the planet . And the planet did not melt to its core.a chain reaction in the atmosphere , would also spread to the ocean , then the crust , and the planet would melt to its core......if you are talking about a nuclear ignition reaction .


But the math is fairly clear here :

No nukes large enough if you are talking either type of ignition : and of course ...hello the Earth is still here ( refer to comet point )
However early in Earths life , I'm sure it did have strikes this great and greater , where it was melted to its core and remolded , or what atmosphere heated and turned into plasma ; reconstituting itself as it cooled ..into some form of ionized gas mixture .
One theory for the moons origin is the impact hypothesis , which surely was a force far greater than that of a minimal reaction threshold .

I think even if you set every nuke on the planet off . The Compton effect always loses more energy due to radiation than gained with a nitrogen reaction... in the air . And hydrogen to helium is different thaN using deuterium .
As far as I am aware every nuke set off at once currently would make like a twenty mile crater . It would be a so - so sized impact equivalent I guess .
They would do more area damage if airbursted in a grid pattern , simultaneously.


Probably make some super hurricanes if thousand set off at one point .
Ignite the atmosphere no .


In theory you would need a ridiculously large nuke to accomplish atmospheric ignition on either level ... on a nuclear level the bomb would have to be so large ..its beyond your imagining .
The math on this has been done, many times. And of course nukes are much more well understood than they were , before one was ever tested , which of course is the origins of this myth . And the bet that occurred
Before the first bomb was tested ..
Hope that helps

I know it's hard to imagine the force a mountain sized object travelling at unimaginable speeds carries with it. But we have been hit by such objects , every nuke combined doesn't even come close to its impact destruction , and the atmosphere is still here . There was an impact possibly even 11,000 years ago ( The Hancock one off of Greenland , Atlantas etc.) that is some 1 million Hiroshima bombs if I recall , maybe 3 million . Yeah atmosphere still here .
Honestly I'm not sure how many Nukes it would take , and what kind of sequence . But I know it's a ridiculous amount .