Primer on concrete basement floor
Joe is correct on this one. The odds of getting all that made it into the concrete off, even with etching solutions, are not good. It is likely training to stain the concrete now will look blotchy.
What makes you think the floor was painted with a primer? My guess is that it was a gray floor paint and this is something you can think about. Floor paints come in lots of nice colors, some can be mixed to match anything, and good ones are quite durable. They do not require a primer (and in fact primers on floors are a bad idea). Benjamin Moore products are the floor paints I know best. The solvent based is urethane reinforced and the waterbased is epoxy reinforced. Once you get the adhesive and residue off, either would be a great choice.
With a little creativity painted floors can be beautiful. You can simulate square or other shaped tiles with some clever paint tape use.
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