Just curious, have you been doing regular water changes all along, or have you just stated doing them since you started noticing the nitrate are up?
Nitrates are cumulative, so unless you have been doing regular water changes all along, it may take a while to lower them.
Also, have you been cleaning filter media regularly? If you are using a canister that goes weeks without cleaning (or any filter) and not cleaning out gunk, that filter and the buildup of gunk becomes a constant spewer of nitrate.
Prime does nothing to lower nitrate..
I find I need to do 30-40% water changes every other day to keep nitrate at my target level, below 10ppm, and have been doing that regime for over 20 years.
And as others have said, unless you are rinsing test tubes thoroughly between tests, a residual film can build up in the tube, and give false results.
I rinse the tubes 3 times before, and 3 times after each test..