This paper studies the achievable throughput performance of the cognitive uplink under a limited primary cooperation scenario wherein the primary base station cannot feed back all interference channel gains to the secondary base station. To cope with the limited primary cooperation, we propose a feedback protocol called K-out-of-N feedback protocol, in which the primary base station feeds back only the KN smallest interference channel gains, out of N of them, to the secondary base station. We characterize the throughput performance under the K-out-of-N feedback protocol by analyzing the achievable multiuser diversity gains (MDGs) in cognitive uplinks for three different network types. Our results show that the proposed feedback mechanism is asymptotically optimum for interference-limited (IL) and individual-power-and-interference-limited (IPIL) networks for a fixed positive KN. It is further shown that the secondary network throughput in the IL and IPIL networks (under both the full and limited cooperation scenarios) logarithmically scales with the number of users in the network. In total-power-and-interference-limited (TPIL) networks, on the other hand, the K-out-of-N feedback protocol is asymptotically optimum for KN = Nδ, where δ ∈ (0,1). We also show that, in TPIL networks, the secondary network throughput under both the limited and full cooperation scales logarithmically double with the number of users in the network. These results indicate that the cognitive uplink can achieve the optimum MDG even with limited cooperation from the primary network. They also establish the dependence of pre-log throughput scaling factors on the distribution of fading channel gains for different network types.