In Halo 4, the Prime skin for the Recruit armor is one of the many special armor skins that you don’t unlock naturally in the game.
The Prime armor skin is only currently available with the purchase of the Collectors Edition of the game. You know how it is though, these “exclusive” items don’t typically stay exclusive very long though, it may be available through DLC in the future.
There are several other nice things that you get with the Collectors Edition though, like the Prime Assault Rifle weapon skin, early access to specializations, as well as some bonus maps.
You might be able to find someone selling their Recruit Prime code on Ebay though.
Check out my other guide for the complete list of unlockable armor sets in Halo 4.