Gamma and X-rays travel in straight lines. At 2000 miles theres no way a nuke from a tower a couple of hundred feet high gets there.
true, although it can be argued that those super high frequency waves can bounce around. I will argue that the fact that those frequencies produced by the Sun and stars are mitigated by our atmosphere and barely reach the Earth, makes it highly unlikely that any of those high intensity waves produced by the atom bomb tests could be effective 2000 miles away traversing the round Earth. But I could be wrong ;-)