Cognitive radio network (CRN) is a promising solution to spectrum scarcity that uses the dynamic spectrum access mechanism to increase the efficiency of the underutilized licensed spectrum. In a CRN, a pair of users exchanges their information at a common unused licensed channel to rendezvous. The rendezvous in all available channels and within the bounded time cycle is a challenging issue in CRNs. In this paper, the primary idea is to construct the channel hopping sequences by using primitive roots of the prime number. For guaranteed rendezvous in CRNs, we design three channel hopping protocols for the symmetric and asymmetric environment in synchronous and asynchronous scenarios of the CRN. Extensive simulation is performed to analyze the throughput, maximum time to rendezvous (MTTR), and average time to rendezvous (ATTR). Simulation results show that our protocols can outperform over the existing protocols and can give significant improvements in terms of MTTR, ATTR, and throughput.