I think he got confused with the terminology - Putin said he tested nuclear-powered Burevestnik, but that's not the same as testing nuclear weapons.
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It was my understanding the US bombs production and management facilities ran tests until simulations were good analogues of what they saw in the real test, at which point it's both cheaper and faster to run simulations.
The only possible reason to run real tests, is for a political communication, although who is receiving it and what it says to them, isn't clear.