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Element 115 and Star Trek?

Theoretically there's an unlimited number of elements. Just we haven't managed to make more than about 118 yet. And all the ones we haven't most likely can only exist for less than a few seconds.

(Predictions about 126 notwithstanding)
 
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Theoretically there's no limit, true. But if the 'trend' of increasing instability of nuclei holds as they're getting heavier I doubt we'll ever see the creation of element, say, 1000 . Barring entirely new (knowledge of) physics, that is.
 
I guess they get more and more unstable because the protons repel each other and overcome the nuclear force
 
I mean, is there a hard limit on how many protons you can fuse together? Or is the only limiter our ability to fuse them?
Well, I don't know. It's a scientific question. Taking the question literally and considering a number of protons that approaches infinity, at some point self-gravitation will become an issue. What happens when the mass of compacted nucleons approaches the Tolman–Oppenheimer–Volkoff limit? The expectation is that it should implode into a black hole. Could such a system have chemical properties? Again, I don't know, but I truly doubt it.
 
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