Will any supercomputer reach 1 zettaFLOP before 2035?
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Historically, it takes about 10 years for the top supercompter's computing power to increase by 3 orders of magnitude. From Wikipedia:

(The red line is the top supercomputer of the time, in gigaFLOPs. The top of the graph is 0.01 zettaflops, so another ~3 dectuplings are required.)

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Depends what the definition of a supercomputer is. Is the bitcoin network a supercomputer?

While the historical trend is remarkable, energy usage might put limits on growth. Current fastest systems consume >20 MW, with all the high cost, heat dissipation issues etc that come with this.