Like all things that enjoy status as currency, it’s relatively scarce. It’s malleable with a reasonably achievable melting point, making it easy to smelt into coins, jewelry, and other valuables. And though it does tarnish, it doesn’t rust as many other metals do, so you don’t run the risk of leaving all your silver in a vault and opening it in twenty years to find the damp got in and rusted away a good chunk of its value. Other than that, it’s just shiny and humans, like crows, are fascinated by glittering, shining things.
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