I disagree with your list. Number four (some claim three) is the Mississippi along with it's longest tributaries, the Missouri etc. The fact that Homo Sapiens has given the longest tributary a different name from the main stem doesn't change the fact of which is the longest river which is basic Geography. By the same token you have omitted no 5, the Yenisei-Angara, 7 the Ob-Irtysh and 10 the Amur-Argun. Also the river which you called "Parana" should be the "Plata".
Agree with CardinalSin. You've included at least two river systems already (Ob-Irtysh, Rio de la Plata-Paraná-Rio Grande) so it's very odd not having Mississippi-Missouri in at 4th place.