Is it possible: 1 Silmaril found: The Arkenstone

[Lindale]

Originally Posted by Eönwë

But Bilbo had the ring at the time, so maybe he was, in some way, immortal.

I beg to differ. Bearing a Ring of power, even if it is the greatest, does not take away mortality. What it does, mainly, is like.... too little butter on too large a toast.

Originally Posted by The Silmarillion, page 305, published by Harper Collins

And thus it came to pass that the Silmarils found their long homes: one in the airs of heaven, and one in the fires of the heart of the world, and one in the deep waters.

There... I think that would disclose any theory that the Arkenstone is a Silmaril. Not withstanding the argument that no mortal hand can touch a Silmaril by virtue of Varda's blessing... and come on. Though Thorin can be considered a "high" dwarf, a Silmaril, something that hallowed, would not suffer such a meager fate. (Meager in the sense that what, it'll just lie forever in the hands of a Dwarvish skeleton in a mountain.)