Well there are several reasons, but this is the coolest: https://en.wikipedia.org/wiki/Island_of_stability

Basically, current theory suggests that once they get to 120 protons or so, they'll start finding stable isotopes again (ones that don't decay for minutes or more). A handle on a door affords pulling, and a hypothesis affords testing, and all that.

Edit: I should add that 115 might actually be within the island, but you'd need far more neutrons, which is currently not feasible.

That's the entire point of the periodic table - what makes it a 'periodic table' rather than 'a list of all the known (or 'found in nature') elements'. When originally conceived it included blank spots for yet un-isolated elements and some predictions about their properties could be made.

You find an element, it goes into the periodic table. Of elements.

> (which I believe could exist elsewhere in the universe...)

They are unlikely to exist elsewhere except for a few moments (not even a second) after a supernova. A regular star will not make them, and they decay extremely fast.

Some of them seem to last much longer than that, or are hypothesized to. If an element has a half-life of a million years, then it probably exists in large quantities throughout the universe. The solar system is a relatively closed system, though, so the elements we see around us have generally been in the solar system for its entire lifetime. So an element would have to last 5+ billion years to exist on earth.

Man-Made or not, At least they have existed. That should be enough to add it to periodic table. There is always a non zero probability that they might exist somewhere else in the universe.

Three reasons:

1- Scientific: Study of superheavy elements is related to the formation of elements in stars and ultimately to the origin of life.

2-Practical: Americium is a man made element which is used in smoke detectors.

3-Nuclear energy: In theory once the island of stability is reached it should be possible to have smaller and more powerful mini nuclear-plants which could fit into a watch.

possible benefits as an energy storage medium once you get to the island of stability.

One that take several order of magnitude more energy to create that it can store? I am in!

The same could easily be said of the battery in your phone, your car, and your laptop. The difference is that energy can be replenished easily, it's storage that's always been the hitch.

yeah by 'possible' I mean 'it would be a stretch, but it's not impossible'. You don't know that there might be a really efficient nucleosynthesis of these guys that we haven't found yet. Plus, there are places where energy is really abundant but hard to capture and store, like, really close to the sun.