Unfortunately, it's not as simple as that. Theoretically, if everyone was using state-of-the-art designs of fast-breeder reactors, we could have up to 300,000 years of fuel. However, those designs are complicated and extremely expensive to build and operate. The finances just don't make it viable with current technology; they would have to run at a huge financial loss.

As for Uranium for sea-water -- this too is possible, but has rapidly diminishing returns that make it financially unviable quite rapidly. As Uranium is extracted and removed from the oceans, exponentially more sea-water must be processed to continue extracting Uranium at the same rate. This gets infeasible pretty quickly. Estimates are that it would become economically unviable within 30 years.

Realistically, with current technology we have about 80-100 years of viable nuclear fuel at current consumption rates. If everyone was using nuclear right now, we would fully deplete all viable uranium reserves in about 5 years. A huge amount of research and development will be required to extend this further, and to make new more efficient reactor designs economically viable. (Or ditch capitalism and do it anyway -- good luck with that!)

Personally, I would rather this investment (or at least a large chunk of it) be spent on renewables, energy storage and distribution, before fusion, with fission nuclear as a stop-gap until other cleaner, safer technologies can take over. (Current energy usage would require running about 15000 reactors globally, and with historical accident rates, that's about one major nuclear disaster every month). Renewables are simpler, safer, and proven ,and the technology is more-or-less already here. Solving the storage and distribution problem is simpler than building safe and economical fast-breeder reactors, or viable fusion power. We have almost all the technology we need to make this work right now, we mostly just lack infrastructure and the will to do it.

I'm not anti-nuclear, nor am I saying there's no place for nuclear, and I think there should be more funding for nuclear research, but the boring obvious solution is to invest heavily in renewables, with nuclear as a backup and/or future option. Maybe one day nuclear will progress to the point where it makes more sound sense to go all in on, say fusion, or super-efficient fast-breeders, etc. but at the moment, it's basically science fiction. I don't think it's a sound strategy to bank on nuclear right now, although we should definitely continue to develop it. Maybe if we had continued investing in it at the same rate for the last 50 years it might be more viable -- but we didn't.

Source for estimates: "Is Nuclear Power Globally Scalable?", Prof. D. Abbott, Proceedings of the IEEE. It's an older article, but nuclear technology has been pretty much stagnant since it was published.