According to the "Red Book", the post-1982 composition of Lincoln cents is:
plating: pure copper
core: 99.2% zinc; 0.8% copper
Total content is 97.5% zinc; 2.5% copper
So the zinc core is reasonably pure, but there is a little copper in it. I wonder how much of the copper plating might dissolve into the zinc when the coin melts. I have melted these coins in the past, but I haven't looked into this in detail. If you want to get the purest possible zinc out of it, it might be wise to remove the copper plating first, perhaps by dipping it in acid until the plating dissolves. (That might dissolve a lot of the zinc as well; perhaps someone else here has a better idea.)
There are other zinc coins around. During World War II, Nazi Germany produced small-denomination zinc coins for Germany and occupied territories. Many of these coins are cheap and plentiful, and most of the surviving ones are in bad shape as they have corroded over the years. I don't know how pure the zinc is, and I haven't tried melting any, but at least they wouldn't have the plating to deal with.
If you want another metal with a low melting point that is relatively inexpensive and easy to obtain, look for bismuth. It will easily melt over a stove, and unlike many heavy metals, its toxicity is low.
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