I have a 1964 penny no mint mark have had it for quite awhile. It has a silver rim on it and looks to be open on the rim a little bit.
It appears someone tried to turn the coin into a jewelry piece at one time or another. Unfortunately it's not an error of any kind. Best of luck, Abram
Looks like it’s in a bezel to make into a necklace. Also looks like the loop to hold a necklace broke off.
All may not be lost, however. I can't tell from the picture, but some jewelry bezels are made of silver and might be worth something as scrap. While on the subject, the shine on your cent looks also to be some sort of plating for jewelry.
In the 3rd photo that's not the rim of the coin. For the 1964 penny to have silver, it would have to be a silver dime planchet that was struck while they were minting pennies. Since the dime is smaller than a penny it would be lighter and all of the details and lettering just inside the rim would be missing (because of the smaller size.)