What would be the consequences of detonating all nuclear weapons on the edge of space?

In today's Dr McNinja, the Vice President of the US (who is also a wizard) detonated all of Russia's nuclear weapons on the edge of space at once:

Since Russia alone has more than enough nukes to end civilization, let's take it Up To Eleven and say Vice President Wizard destroys all other nuclear weapons as well, citing that "noone, not even President Radical, should need this much radness".

According to the most recent estimates, there are over 17,000 nuclear weapons. What would happen to Earth if all these weapons were detonated all at once on the edge of space (which we set at 100 km high for the sake of clarity)?

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What would be the consequences of detonating all nuclear weapons on the edge of space?

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