An adapted version of the annealing algorithm to identify primitive paths of a melt of ring polymers is presented. This algorithm ensures that the primitive path length becomes zero for nonconcatenated rings, and that no entanglements are observed. The bond-fluctuation model was used to simulate ring-linear blends with N=150 and 300 monomers. The primitive path length and the average number of entanglements of the linear component were found to be independent of the blend composition. In contrast, the primitive path length and the average number of entanglements on a ring molecule increased approximately linearly with the fraction of linear chains, and for large N , they approached values comparable with linear chains. Threading of ring molecules by linear chains, and ring-ring interactions were observed only in the presence of linear chains. It is conjectured that for large N , these latter interactions facilitate the formation of a percolating entangled network, thereby resulting in a disproportionate retardation of the dynamical processes.