What kind of capacitor should I use on my Pioneer Premire PRS-D2000SPL 4000 watt amp?

1 farad for every 1000watts of amp. so 4.0 farad cap would be right. I would just go with a spare car battery in the trunk. for some reason this usually works better. If the amp is making your lights dim, a cap or battery might only make it worse. you might need to upgrade your alternator and big 3 if your gonna have that much power running