Memtest is what you want. Note that once you start it, it will run continuously until you kill it, but you want to be sure that you allow it to complete several (at least 3 or 4) complete cycles in order to have confidence in the results. Note also that each cycle consists of several different tests (eg, writing all zeros, all ones, FF00, 00FF, etc) and that the more RAM you have, the more time it will take to complete each cycle. As a (very) general guideline, a full cycle may take anywhere from between 30 to 60 minutes to complete, so my recommendation would be to start memtest before you go to sleep, and let it run overnight.
Most RAM is actually pretty high quality, and errors are relatively uncommon. However, if an error is found, the only option is to replace the stick. Good luck with it -- J.W.