I don't know how authorized I am to judge this, but this is my opinion on the matter.
These 4 rappers I am about to name should be on every greatest rappers list. They each combined unique style, unique and incredible lyrics, and all around great ability while managing to be hip-hop and still me mainstream.
-He made 14ish albums in the 4 or 5 years he was alive and in the game. Most rappers can't do that in their career. He made songs to dance to, political songs, and songs telling stories. He did all that while sounding very pleasant, having controversial issues every day and having millions waiting for his orders. Those things make him a must have on any greatest rappers list.
-Undoubtly one of the best. His skill freestyling and story telling is by far the best (in my opinion) that hip-hop music will ever see. Though his career was short lived, he will always be remembered and lived on through his music.
-Nas is my favorite rapper. Since his first release (Illmatic) to his work with the Firm to his last release (Street's Disciple) Nas has been one of the best. The lyrics of every song and the way he flows is unique and will never be seen again by a new rapper. He also managed to fall off the charts, then come back with one of the best albums (Stillmatic). From beef with BIG, beef with 2pac, and beef with Jay-Z, Nas has remained poised and great. Listen to any of his albums and you'll see why he is one of the greatest.
-This may seem shocking but I beleive Eminem is one of the all time greats. If you listen to the Slim Shady LP, The Marshall Mathers LP, and The Eminem Show, you'll see his greatness. His songs can make you laugh, or fire you up to a point beyond beleif. He can also fire back at any critism (Who Knew, Cleanin' Out My Closet, ect.). Eminem has dealt with protestors and being a white rapper. Buy his albums, you will not be dissapointed.
There are many other rappers who are great, perhaps better, but I beleive these four must be on every top 10 list.