The Way of Kings Prime is the original draft of The Way of Kings written in 2002. It is completely different to the version released back in 2011, and is not canon to the Cosmere universe. Brandon Sanderson released this version as a extra goodie during The Way of Kings 10th Anniversary Leatherbound Edition Kickstarter

" The Way of Kings Prime , was written in 2002 and is basically an alternate version of The Way of Kings , which was published by Tor Books in 2010. The Way of Kings Prime is very different from the published book. Think of it as set in a different universe with a completely different plot. If you haven’t read the 2010 canonical version, please read that one first. " -- from author's website (emphasis mine)