You can try installing the fan to the Motherboard case fan connector (three or four pins) and see if it runs correctly. If it doesn't you probably have a bad Wraith Prism Fan cooler or it is installed incorrectly.
From your Gigabyte Manual: Try connecting it to SYS_FAN1 and see if it work correctly.
Make sure when you installed the Wraith Prism it is not installed in a way that prevents the fan from turning. Can you turn the Wraith Fan easily by hand or is it kinda tight or slightly hard to turn?
Or you can remove the Wraith CPU Cooler and go to another computer and connect the Fan to that motherboard and see if it run correctly. If it is the same then you have a bad Fan, if runs correctly than the fan is probably good. Try reinstalling the Wraith again and see if the problem occurs again. It might just be a incorrect installation of the Wraith Prism on the CPU.
You can also connect a Case fan to the CPU Fan connector and see if the fan turns on. Even though the Case fan may only have 3 pins it will fit on a 4 pin Motherboard connector except it won't have PWM control and it should run at 100%.
I have a 3 pin case fan connected to my motherboard's 4 pin CPU AUX Fan connector which I installed as a second fan on my CPU Cooler. It runs at 100% all the time which is fine with me.
EDIT: By connecting a Case fan to the CPU FAN connector on the Motherboard and it runs correctly this should tell you if the motherboard is the problem. Most likely it is the CPU Wraith Fan.
