In [0], they give a figure of 5-6 years for actual construction. Add in a year or 2 for regulatory and other delays, and we're looking at 2027-2029-ish before we see a single megawatt of electricity out of them. What's more, there is probably only enough uranium to last about 5 years, if we could wave a magic wand and replace all existing power plants with nuclear [1]. Moreover, the plants themselves also have a finite lifetime of 40-60 years [ibid].
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[0]: https://en.wikipedia.org/wiki/Economics_of_nuclear_power_pla...
https://phys.org/news/2011-05-nuclear-power-world-energy.htm...