These come in gold as well as silver. They are part of a large body of silver medallions known as Art Rounds. You can read more about them at this CoinQuest link.
Engelhard is one of the biggest (perhaps the biggest) private producer of bullion products. They are very reliable and very trustworthy. Not surprisingly, their rounds are worth their weight in bullion. For silver, at this writing, that is $30 per troy ounce. For gold it is $1645 per troy ounce. These prices change every day. Be sure to look up the current price, as it could be MUCH different. Our favorite web site for precious metal values is kitco.com.
The prospector image is especially appealing for precious metal rounds, so you find many different patterns. The reputation of the company producing the rounds is important. If it is Engelhard, as discussed above, everything's fine. If it is Acme AAA+ Super-Duper Silver Company, I'd question the silver content.
If I had these to sell, I'd sell them as close to bullion price as I could. I would search for a buyer who would pay the highest price (an auction on eBay, for example). However, if I were looking to buy gold or silver, I would not buy American Prospector rounds. Why? Because rounds can be easily counterfeited. Of course all coins can be counterfeited, but it is much less likely to encounter a fake American Silver Eagle coin than a fake American Prospector round. The ASE is guaranteed by the US government. The American Prospector is guaranteed by a private firm which is much smaller than the government. I am all for capitalism, but not when it comes to bullion coins. Bullion coins issued by reliable governments are the way to go.