Now it gets a bit more complex sadly
Double check everything is at stock: RAM timings are correct for instance. It's unlikely to be causing the issue, but I'd also update the BIOS if there is a newer version.
Prime shouldn't really error at all.
I'd recommend giving the Intel burn test a shot:
http://www.xtremesystems.org/forums/...esting-program
It will probably also cause errors faster than Prime.
The other obvious culprits are mobo and PSU (it could be dropping the voltage when under sustained heavy load). Sadly temperamental issues like this are a nightmare to solve