What type of mem, and at what timings are you running, and what are the mem voltages?
A little system info would help....like what processor you are running, what vcore, mainboard, etc.
If your mem is running stock, then you should look into the processor...excessive heat,
or excessive volts can make prime fail.
Maybe what you should try is to run the mem as fast and tight as you can while clocking down the cpu and still get it to post, and run Memtest86+ and see if you run into any problems..in other words, try running the cpu at stock and up the memory multiplier to see where your memory craps out...then you can eliminate the memory as the problem.
Hope this helps,
Doc